Dynamic Models for Exploring the Resilience in Territorial Scenarios

The present paper focuses on the role covered by dynamic models as support for the decision-making process in the evaluation of policies and actions for increasing the resilience of cities and territories. In recent decades, urban resilience has been recognized as a dynamic and multidimensional phenomenon that characterizes urban and metropolitan area dynamics. Therefore, it may be considered a fundamental aspect of urban and territorial planning. The employment of quantitative methods, such as dynamic models, is useful for the prediction of the dynamic behavior of territories and of their resilience. The present work discusses the system dynamics model and the Lotka–Volterra cooperative systems and shows how these models can aid technicians in resilience assessment and also decision makers in the definition of policies and actions, especially if integrated in wide evaluation frameworks for urban resilience achievements. This paper aims to provide an epistemological perspective of the application of dynamic models in resilience assessment, underlying the possible contribution to this issue through the analysis of a real case study and methodological framework. The main objective of this work is to lay the basis for future compared applications of these two models to the same case study.


Introduction
Cities and territories across the world are increasingly exposed to a number of risks, hazards and stresses [1,2]. These affect all urban system dimensions, from the environmental to the social and economic [3,4]. Therefore, the concept of resilience is increasingly being used in urban and territorial policy in order to prepare urban systems for hazards and uncertainties [2,5,6]. Urban resilience is defined as a dynamic and multidimensional phenomenon that characterizes metropolitan areas as complex systems at all scale dimensions [7][8][9]. Urban resilience is related to several disciplines and domains, such as risk reduction, climate change and adaptation strategy. More recently, urban resilience has also been involved in the definition of policies and actions for achieving urban and territorial purposes [2,7,9]. The guidelines for increasing urban resilience are effective planning procedures-the identification and prioritization of which require the involvement of experts with specific competences and from different disciplines in the decision-making process [10]. This paper explores the role of dynamic models in support of the definition of policies and actions to enhance urban resilience. These models belong to the family of mathematical modelling, which is able to simulate the behavior of complex systems over time by using a set of Ordinary Differential Equations (ODEs). In this paper, dynamic models are investigated according to methodological background and operative characteristics. The main aim is to consider their general characteristics and peculiarities  Holling, 1973 Ecology "The ability of these systems to absorb changes of states variables, driving variables, and parameters, and still persist" (p. 17). Dynamic Pimm, 1984 Ecology "How fast the variables return towards their equilibrium following a perturbation" (p. 322). Static Carpenter et al., 2001 Social-ecological systems "The magnitude of disturbance that can be tolerated before a socioecological system (SES) moves to a different region of state space controlled by a different set of processes" (p. 765).
Dynamic Adger, 2000 Geography "The ability of groups or communities to cope with external stresses and disturbances as a result of social, political and environmental change" (p. 347). Dynamic Rose, 2007 Economics "The speed at which an entity or system recovers from a severe shock to achieve a desired state" (p. 384). Dynamic Fiksel, 2006 Systems engineering "The capacity of a system to tolerate disturbances while retaining its structure and function" (p. 16). Dynamic Zhu and Ruth, 2013 Industrial ecology "The ability [for industrial ecosystems] to maintain their defining feature of eco-efficient material and energy flows under disruptions" (p. 74). Dynamic

Zeng and colleagues, 2013
Networks "The critical threshold at which a phase transition occurs from normal state to collapse" (p. 12). Static Ouyang, 2014 Engineering "The joint ability of a system to resist (prevent and withstand) any possible hazards, absorb the initial damage, and recover to normal operation" (p. 53). Static Adger, 2000 Social resilience "Ability of groups or communities to cope with external stresses and disturbances as a result of social, political and environmental change" (p. 347). Static From these aspects, this paper aims to focus on the definition of urban resilience to highlight the communalities and differences in academic and policy debate. The objective of this analysis is to highlight the malleability of the urban resilience concept and to stress on its implications in policy definition [47]. Table 2 lists a series of definitions on urban resilience by considering academic and political references with the purpose to better understand what the needs and the tools are to be employed as support of the decision-making process for building resilient cities.
These different definitions are listed to underline their communalities and differences in their meaning. They are different from the formal point of view. However, all these definitions concern with the multidimensional and transformative approach of urban resilience [7]. They also focus the attention on the dynamic behavior of resilience processes both in spatial and time scales [6].
This means that building urban resilience requires looking at urban and territorial systems holistically. It is necessary to understand cities in all dimensions and identify interdependencies and risks they may face.
For this application, the definition of Meerow et al. [32] has been considered for its holistical view of urban systems and its attention to both spatial and temporal scales.
Nowadays, the main problems which regard the design of policies and strategies to build urban resilience lies in the difficulty of evaluating this process over time and in spatial dimensions.
This paper explores the DMs in order to verify their efficiency in application in scenario planning, in order to find suitable tools which may support decision makers to define and prioritize strategies and policies to enhance urban resilience.

Dynamic Models in the Decision-Making Process
The definition of effective policies needs to be informed by a holistic understanding of the system processes. Their complex interactions and the ways they respond to various changes and inputs have to be evaluated. In this sense, models are, in general, seen as useful tools to aid actors and stakeholders to analyze alternative possible solutions and assess their outcomes. In fact, models generally integrate knowledge developed across a broad range of fields. They are generally used for different purposes. In this section, we focus on their application in management and treatment of uncertainty. Dynamic models cover a number of different methods and approaches able to simulate the behavior of future scenarios. Among the different methods belonging to the family of mathematical modelling, the present paper considers the system dynamics model (SDM) and the Lotka-Volterra model (LV). In this section, the methodological background and the state of art are investigated for both the SDM and LV models with the aim to highlight their fundamental role in the prediction of Sustainability 2020, 12, 3 5 of 19 possible future scenarios for exploring urban resilience. Moreover, an illustration of some relevant applications is proposed in order to explain the methodological steps for the applications and the type of results that can be obtained.

Urban Simulation Models
In this paragraph, an overview of the urban simulation methods is given. The selected urban simulation methods are here discussed as reliable support in the decision-making process, especially in the case of designing urban and territorial transformations that may solicitate perturbations on the system on its resilience. Starting from a literature review [48], different simulation models have been selected to be analyzed. Table 3 lists the considered models and describes them, considering field and purpose of applications, types of data, treatment of space, time and uncertainty. This overview of different models has been useful to support the choice of the model to experiment and use in investigating the urban resilience.

Methodological Background and State of Art
System dynamics model (SDM) is an operative approach for helping reveal temporal behavior of complex systems considering their non-linearity, time-delay and multi-loop structure [49,50]. SDM is based on the System Dynamics approach which was introduced by Forrester [51,52] for investigating the feedback information of industrial systems and improving the organizational form [53]. SDM is an effective tool for modelling intersectional dynamics, such as the prey-predator models [54,55]. The relationships and interactions between variables in the system are analyzed by this tool (SDM) in order to simulate its dynamic evolutions in terms of processes, information and organizational boundaries [50].
In SDM, complex and dynamic systems are described both in qualitative/conceptual and quantitative representations. The qualitative modelling is performed by the causal loop diagram ( Figure 1). This tool is used to graphically represent the feedback loops structure of the system. Causal loop diagram (Figure 1) describes the basic mechanism of the system, in order to represent the causes of its dynamics behavior over time [50,56]. The relationships between the variables can be either positive or negative, as shown in Figure 1. A positive relationship signifies that variables change equally. By contrast, a negative relationship means that the variables change inversely.
Quantitative modelling is represented by stock and flow diagram ( Figure 2). Stock is the first basic building block in SDM and it represents the variable which describes the condition of the system at any particular time [12,50,[57][58][59]. Flow is the second block in SDM and it tells how stocks change over time. quantitative representations. The qualitative modelling is performed by the causal loop diagram ( Figure 1). This tool is used to graphically represent the feedback loops structure of the system. Causal loop diagram (Figure 1) describes the basic mechanism of the system, in order to represent the causes of its dynamics behavior over time [50,56]. The relationships between the variables can be either positive or negative, as shown in Figure 1. A positive relationship signifies that variables change equally. By contrast, a negative relationship means that the variables change inversely. Quantitative modelling is represented by stock and flow diagram ( Figure 2). Stock is the first basic building block in SDM and it represents the variable which describes the condition of the system at any particular time [12,50,[57][58][59]. Flow is the second block in SDM and it tells how stocks change over time. From a mathematical point of view, stock and flow diagrams are represented by first-order finite difference equations. These allow to simulate the dynamic behavior of the system. The differential equations which characterize stock and flow can be expressed as: and this integration equation in the differential equation form is: The most frequent type of possible system behavior can be summarized as follows [60]: • Exponential growth or decline, which is characterized by only positive or only negative feedbacks; • Goal-seeking behavior, which is created by first-order negative feedback; equally. By contrast, a negative relationship means that the variables change inversely. Quantitative modelling is represented by stock and flow diagram ( Figure 2). Stock is the first basic building block in SDM and it represents the variable which describes the condition of the system at any particular time [12,50,[57][58][59]. Flow is the second block in SDM and it tells how stocks change over time. From a mathematical point of view, stock and flow diagrams are represented by first-order finite difference equations. These allow to simulate the dynamic behavior of the system. The differential equations which characterize stock and flow can be expressed as: and this integration equation in the differential equation form is: The most frequent type of possible system behavior can be summarized as follows [60]: • Exponential growth or decline, which is characterized by only positive or only negative feedbacks; • Goal-seeking behavior, which is created by first-order negative feedback; From a mathematical point of view, stock and flow diagrams are represented by first-order finite difference equations. These allow to simulate the dynamic behavior of the system. The differential equations which characterize stock and flow can be expressed as: and this integration equation in the differential equation form is: The most frequent type of possible system behavior can be summarized as follows [60]: • Exponential growth or decline, which is characterized by only positive or only negative feedbacks; • Goal-seeking behavior, which is created by first-order negative feedback; • S-shaped growth. This behavior, over time, is created by a combination of positive and negative feedback loops. In this case, both loops struggle for dominance until the struggle ends with a long-term equilibrium; • Oscillations. This is one of the most common types of dynamic behaviors in the world and it can have different forms, such as (1) sustained oscillations; (2) damped oscillations; (3) exploded oscillations; (4) chaos. The structure that creates oscillations is a combination of negative feedback loops and delay.
Currently, SDMs are used to support policy design and management for sustainable development in those fields characterized by a high level of uncertainty, such as transport management [58,61,62], land use [63], waste management [59] and also sustainable urban development [13,57,64,65]. In the last few decades, an increase of SDM application has been observed in literature [66], especially in the urban development field. Table 4 lists some of the prevalent SDM applications with particular attention to urban system and urban development. Table 4 shows that SDM is an effective tool for supporting the evaluation of different development scenarios' performance, considering their possible effects over time. For this reason, it is considered as a useful tool to support decision makers in setting policies.

Illustrative Example
In this section, the application of SDM developed by Tan et al. [13] to the case study of Beijing (China) is considered for the illustration of the fundamental steps of the procedure and the typology of results that the method is able to deliver. In [13], the SDM are applied to simulate the urban sustainability performance of the city, considering three different development scenarios. The SDM has been developed following these steps: (1) identifying the key variables by a review of urban sustainability indicators; (2) building the stock and flow diagram to identify the relationships between the variables; and (3) simulating different scenarios. Figure 3 shows the stock and flow diagram of the social sector. In particular, the stocks of the diagram are (1) Total population, (2) Urbanization rate, and (3) GDP, whereas all the other variables represent the flows. The diagram also shows the relationships that exist among the considered variables. As an example, we can consider the relationship that exists between "local government annual fiscal revenue" and "financial educational investment". That means the investment in educational fields strictly depends on the availability of government financial resources. It appears clear that the SDM model tries to describe the real-world functioning through its stock and flow diagram, based on real behavior.    Figure 4 illustrates the results of SDM scenarios simulation, gathered by the stock and flow diagram in Figure 3.
These outcomes reveal the evolution of the indicators over time, referred to three different development scenarios (Figure 4). Simulation has been obtained by mathematical equations. For instance, Equation (2) illustrates the equation of annual household waste emission: HWS = DSWE per capita * Total population (Unit: ten thousand tons) (2) where: (1) "HWS" is the annual household's waste emission; (2) "DSWE" is the domestic solid waste emission.  These outcomes reveal the evolution of the indicators over time, referred to three different development scenarios (Figure 4). Simulation has been obtained by mathematical equations. For instance, Equation (2) illustrates the equation of annual household waste emission: HWS = DSWE per capita * Total population (Unit: ten thousand tons) (2) where: (1) "HWS" is the annual household's waste emission; (2) "DSWE" is the domestic solid waste emission.
Specifically, in Figure 5, the SDM simulation results are referred to (1) "Current scenario" which represents no change in urban development actions; (2) "High speed scenario" that is characterized by a faster urbanization process and a higher economic growth rate; and (3) "Slow scenario" in which the urbanization process is limited. Specifically, in Figure 5, the SDM simulation results are referred to (1) "Current scenario" which represents no change in urban development actions; (2) "High speed scenario" that is characterized by a faster urbanization process and a higher economic growth rate; and (3) "Slow scenario" in which the urbanization process is limited.

Methodological Background and State of Art
Lotka-Volterra models (LV) are generally employed in the field of landscape ecology for exploring the prey-predator interactions [67,68]. These models have been integrated only recently in wide integrated evaluation frameworks to better interpret non-linear dynamics of territories, and so, their capability to adapt themselves to natural and/or anthropic disturbances and disasters, thus going beyond the analyses of ecological systems [55].
In fact, the aim of Lotka-Volterra models within territorial and urban planning consist in being a support for the investigation of a given environmental system N and the prediction of possible future transformations.
As shown in Equation (3), these models assume the form of a pair of non-linear Ordinary Differential Equations (ODEs) [69]: where a 1 and a 2 are Malthusian coefficients that consider the dynamic evolutions of the populations p 1 and p 2 in terms of natality and mortality rates; b 1 and b 2 are Verhulst coefficients that considers scarce territorial resources, with b 1 , b 2 < 0. These coefficients are proportional to carrying capacity (c 1 , c 2 ) with b 1 = e c 1 and b 2 = e c 2 ; a 12 and a 21 are the terms that characterize the interaction between the two populations. In this way, we may consider three cases that correspond to three types of Lotka-Volterra models [69]: • if a 12 , a 21 > 0, p 1 benefits from the presence of the second state variable p 2 , then Lotka-Volterra models are defined as "cooperative"; • if a 12 , a 21 < 0, the first state variable competes with the second state variable, then Lotka-Volterra models are "competitive"; • if a 12 < 0 (prey), a 21 > 0 (predator), it means that the two variables are opposite, then Lotka-Volterra models are "prey/predator".
Lastly, I 1 and I 2 represent the rates of in-migration and out-migration. Among the types of Lotka-Volterra models, this paper is focused on Lotka-Volterra cooperative type models. An example of a Lotka-Volterra cooperative type model for the state variables V and E is: where In Table 5, a number of literature contributions are listed, in that the outcome of Lotka-Volterra systems may be interpreted as a resilience factor. More in details, Finotto and Monaco [70] and Gobattoni et al. [71,72] are generally used for developing stability analyses on ecological sectors, thus predicting future possible equilibrium states; Monaco and Servente [69] are used to simulate the population's mobility and Monaco [73] integrates a synthetic index calculated through a system of indicators for investigating the population's mobility with respect to Gross Leasable Areas (GLAs); Assumma et al. [74,75] predicts the population's flow over time in rural landscapes with respect to the economic attractiveness; Assumma et al. [76] simulates the dynamics related to economic attractiveness and ecological quality as resilience factor. Therefore, Lotka-Volterra models have been employed at different spatial scales with different purposes, thus obtaining useful insights, such as in the field of landscape ecology and landscape economics [77]. In this section, a recent application on a supra-municipal context in Piedmont region (Italy) is proposed [76].

Illustrative Example
In Assumma et al. [76], an extension of a Lotka-Volterra model by Monaco and Rabino [78] was developed (Equation (5)) with the aim at simulating population dynamics as a resilient factor related to ecological and economic states for the territory of the Monferrato Ovadese in Southern Piedmont (Italy). The case study under investigation was intended as a multi-pole territorial system, where the poles refer to 37 municipalities that were grouped into 11 territorial clusters.
where P' i is the state variable of the population i; A represents a synthetic index of ecological quality and economic attractiveness calculated for the poles i and j; d ij consists in the distance recorded between the poles i and j, whereas d M measures the recorded highest distance between the poles; and S i is the carrying capacity, that is intended as the threshold number of people in a given pole. It has to be noticed that the parameter A i was calculated by considering a system of landscape economic indicators and a system of ecological indicators, according to a Multicriteria approach (for more, please see [74,79,80]). The considered systems of indicators and their indices aim to calculate a super-index that measures the overall attractiveness of the territory by considering the ecological quality and the economic attractiveness. The index of overall attractiveness was integrated into the Lotka-Volterra model in order to simulate the trends of populations with respect to both ecological and economic states. The results obtained by an evaluation procedure based on a Multicriteria approach are illustrated in Figure 5, whereas the results of the Lotka-Volterra model simulations are shown in Figure 6.
The results of the model are useful for predicting possible future evolutions about the mobility of resident populations. As shown in Figure 6, the first group of populations (P1-P4) behave similarly in the transitory time, with an exception for population (P1) because of a consistent degrowth. The second group of populations (P5-P8) behave differently; in fact, the population of the cluster of Novi Ligure (P5) is interested by a slight degrowth, the population of the cluster Lerma (P6) grows significantly and finally, populations of the clusters of Ovada and Predosa (P8 and P9) show similar growing behaviors. In this sense, the poles were intended as receptors of the considered territory that absorb and evolve toward a new state, as already said, with respect to ecological and economic aspects. The predicted scenarios on population dynamics were interpreted as the effects of the non-linear interactions between the ecological and economic components with the multi-pole territorial system. In fact, when the multi-pole territorial system shows a good equilibrium between ecological and economic aspects, the population grows significantly, as in the case of the population of the cluster of Predosa (P8); whereas when one of the considered components records negative values, the population decreases, as in the case of the population of the cluster of Novi Ligure (P1).   The results of the model are useful for predicting possible future evolutions about the mobility of resident populations. As shown in Figure 6, the first group of populations (P1-P4) behave similarly in the transitory time, with an exception for population (P1) because of a consistent degrowth. The second group of populations (P5-P8) behave differently; in fact, the population of the cluster of Novi Ligure (P5) is interested by a slight degrowth, the population of the cluster Lerma (P6) grows significantly and finally, populations of the clusters of Ovada and Predosa (P8 and P9) show similar growing behaviors. In this sense, the poles were intended as receptors of the considered territory that absorb and evolve toward a new state, as already said, with respect to ecological and economic aspects. The predicted scenarios on population dynamics were interpreted as the effects of the nonlinear interactions between the ecological and economic components with the multi-pole territorial system. In fact, when the multi-pole territorial system shows a good equilibrium between ecological and economic aspects, the population grows significantly, as in the case of the population of the cluster of Predosa (P8); whereas when one of the considered components records negative values, the population decreases, as in the case of the population of the cluster of Novi Ligure (P1).

How Can These Models Contribute for Building Resilient Systems?
SDMs constitutes a family of tools that uses the ODEs to predict the performance of a given criterion over time and more in general cycles that depends on a number of factors, whereas the Lotka-Volterra are models that face more complex problems.

How Can These Models Contribute for Building Resilient Systems?
SDMs constitutes a family of tools that uses the ODEs to predict the performance of a given criterion over time and more in general cycles that depends on a number of factors, whereas the Lotka-Volterra are models that face more complex problems.
The link between the SDMs and LV models is pointed out by Crookes and Blignaut [55], who stated that prey-predator models are suitable to be used in system dynamics models [54], also finding some applications in the field of economics [81,82], ecology (see e.g., [83,84]), and in multidimensional sectors in a supply chain [85]. The most important commonality of these two methods, especially regarding to the assessment of urban resilience referred to in urban and transformation strategies, is that both the models can consider the interactions between the different elements and sectors in urban contexts. This characteristic represents the real peculiarity of these systems for evaluating urban resilience, in fact, there are no consolidated assessment methods in literature on urban resilience [86].
In this sense, a clarification about specific characteristics of SDM and LV has to be done, before the analysis of their possible contribution in decision-making for resilience enhancing. Indeed, beyond the similarity which concerns the mathematic bases, these models are quite different.
As shown in Table 6, a comparison matrix has been structured with the aim to investigate both commonalities and differences between the SDM and LV models in orienting decision problems related to urban planning, with specific attention to the resilience enhancement.

Nature
Essence and characters * starting from the state of art conditions (t0) [50]. In this sense, both the SDM and the LV models are useful supports for the decision makers for identifying the most critical areas and adopting specific policies and interventions. • Scale refers to the application of dynamic models at different scales. Moreover, the SDM considers a system as a whole, analyzing and focusing on its components and sub-components. In fact, SDMs are mostly applied to municipal or metropolitan scales. LV models are generally employed to provincial and sub-regional scales and to those territories with a rural vocation.

Nature
Essence and characters *

Input
Use of qualitative and quantitative data Participatory process Use of different spatial scales

Scenario simulation
Time scale starting from the state of art conditions (t0) [50]. In this sense, both the SDM and the LV models are useful supports for the decision makers for identifying the most critical areas and adopting specific policies and interventions.
• Scale refers to the application of dynamic models at different scales. Moreover, the SDM considers a system as a whole, analyzing and focusing on its components and sub-components. In fact, SDMs are mostly applied to municipal or metropolitan scales. LV models are generally employed to provincial and sub-regional scales and to those territories with a rural vocation.

Input
Use of qualitative and quantitative data starting from the state of art conditions (t0) [50]. In this sense, both the SDM and the LV models are useful supports for the decision makers for identifying the most critical areas and adopting specific policies and interventions. • Scale refers to the application of dynamic models at different scales. Moreover, the SDM considers a system as a whole, analyzing and focusing on its components and sub-components. In fact, SDMs are mostly applied to municipal or metropolitan scales. LV models are generally employed to provincial and sub-regional scales and to those territories with a rural vocation.

Nature
Essence and characters *

Input
Use of qualitative and quantitative data Participatory process Use of different spatial scales

Scenario simulation
Time scale starting from the state of art conditions (t0) [50]. In this sense, both the SDM and the LV models are useful supports for the decision makers for identifying the most critical areas and adopting specific policies and interventions.
• Scale refers to the application of dynamic models at different scales. Moreover, the SDM considers a system as a whole, analyzing and focusing on its components and sub-components. In fact, SDMs are mostly applied to municipal or metropolitan scales. LV models are generally employed to provincial and sub-regional scales and to those territories with a rural vocation.

Nature
Essence and characters *

Input
Use of qualitative and quantitative data Participatory process Use of different spatial scales

Scenario simulation
Time scale Participatory process • Scenario planning refers to the prediction of future scenarios and the definition for each scenario of objectives and strategies. Both SDM and LV models allow to predict the way variables evolve, starting from the state of art conditions (t0) [50]. In this sense, both the SDM and the LV models are useful supports for the decision makers for identifying the most critical areas and adopting specific policies and interventions.
• Scale refers to the application of dynamic models at different scales. Moreover, the SDM considers a system as a whole, analyzing and focusing on its components and sub-components. In fact, SDMs are mostly applied to municipal or metropolitan scales. LV models are generally employed to provincial and sub-regional scales and to those territories with a rural vocation.

Nature
Essence and characters *

Input
Use of qualitative and quantitative data Participatory process Use of different spatial scales

Scenario simulation
Time scale visualizing spatially the output of the dynamic model in a final map and therefore, identifying specific policies and solutions. • Scenario planning refers to the prediction of future scenarios and the definition for each scenario of objectives and strategies. Both SDM and LV models allow to predict the way variables evolve, starting from the state of art conditions (t0) [50]. In this sense, both the SDM and the LV models are useful supports for the decision makers for identifying the most critical areas and adopting specific policies and interventions.
• Scale refers to the application of dynamic models at different scales. Moreover, the SDM considers a system as a whole, analyzing and focusing on its components and sub-components. In fact, SDMs are mostly applied to municipal or metropolitan scales. LV models are generally employed to provincial and sub-regional scales and to those territories with a rural vocation. Table 6. Lotka-Volterra models and System Dynamic Models: summarizing comparison matrix (Authors' elaboration, 2019).

Nature
Essence and characters *

Input
Use of qualitative and quantitative data Participatory process Use of different spatial scales

Scenario simulation
Time scale Use of different spatial scales platforms (e.g., QGIS Python console) and to get a spatial visualization of the output. Despite the requirement of specific competences to manage DMs in GIS environment, the users may support decision makers in better interpreting certain dynamics related to urban resilience by visualizing spatially the output of the dynamic model in a final map and therefore, identifying specific policies and solutions. • Scenario planning refers to the prediction of future scenarios and the definition for each scenario of objectives and strategies. Both SDM and LV models allow to predict the way variables evolve, starting from the state of art conditions (t0) [50]. In this sense, both the SDM and the LV models are useful supports for the decision makers for identifying the most critical areas and adopting specific policies and interventions.
• Scale refers to the application of dynamic models at different scales. Moreover, the SDM considers a system as a whole, analyzing and focusing on its components and sub-components.
In fact, SDMs are mostly applied to municipal or metropolitan scales. LV models are generally employed to provincial and sub-regional scales and to those territories with a rural vocation. Table 6. Lotka-Volterra models and System Dynamic Models: summarizing comparison matrix (Authors' elaboration, 2019).

Nature
Essence and characters *

Input
Use of qualitative and quantitative data Participatory process Use of different spatial scales

Scenario simulation
Time scale of objectives and strategies. Both SDM and LV models allow to predict the way variables evolve, starting from the state of art conditions (t0) [50]. In this sense, both the SDM and the LV models are useful supports for the decision makers for identifying the most critical areas and adopting specific policies and interventions. • Scale refers to the application of dynamic models at different scales. Moreover, the SDM considers a system as a whole, analyzing and focusing on its components and sub-components. In fact, SDMs are mostly applied to municipal or metropolitan scales. LV models are generally employed to provincial and sub-regional scales and to those territories with a rural vocation. language (e.g., QGIS and Python). Actually, the integration of DMs simulation results into GIS is developed by users in specific plug-ins (e.g., PANDORA 3.0 [97]) or by using specific coding platforms (e.g., QGIS Python console) and to get a spatial visualization of the output. Despite the requirement of specific competences to manage DMs in GIS environment, the users may support decision makers in better interpreting certain dynamics related to urban resilience by visualizing spatially the output of the dynamic model in a final map and therefore, identifying specific policies and solutions. • Scenario planning refers to the prediction of future scenarios and the definition for each scenario of objectives and strategies. Both SDM and LV models allow to predict the way variables evolve, starting from the state of art conditions (t0) [50]. In this sense, both the SDM and the LV models are useful supports for the decision makers for identifying the most critical areas and adopting specific policies and interventions.
• Scale refers to the application of dynamic models at different scales. Moreover, the SDM considers a system as a whole, analyzing and focusing on its components and sub-components.
In fact, SDMs are mostly applied to municipal or metropolitan scales. LV models are generally employed to provincial and sub-regional scales and to those territories with a rural vocation. language (e.g., QGIS and Python). Actually, the integration of DMs simulation results into GIS is developed by users in specific plug-ins (e.g., PANDORA 3.0 [97]) or by using specific coding platforms (e.g., QGIS Python console) and to get a spatial visualization of the output. Despite the requirement of specific competences to manage DMs in GIS environment, the users may support decision makers in better interpreting certain dynamics related to urban resilience by visualizing spatially the output of the dynamic model in a final map and therefore, identifying specific policies and solutions. • Scenario planning refers to the prediction of future scenarios and the definition for each scenario of objectives and strategies. Both SDM and LV models allow to predict the way variables evolve, starting from the state of art conditions (t0) [50]. In this sense, both the SDM and the LV models are useful supports for the decision makers for identifying the most critical areas and adopting specific policies and interventions.
• Scale refers to the application of dynamic models at different scales. Moreover, the SDM considers a system as a whole, analyzing and focusing on its components and sub-components.
In fact, SDMs are mostly applied to municipal or metropolitan scales. LV models are generally employed to provincial and sub-regional scales and to those territories with a rural vocation. language (e.g., QGIS and Python). Actually, the integration of DMs simulation results into GIS is developed by users in specific plug-ins (e.g., PANDORA 3.0 [97]) or by using specific coding platforms (e.g., QGIS Python console) and to get a spatial visualization of the output. Despite the requirement of specific competences to manage DMs in GIS environment, the users may support decision makers in better interpreting certain dynamics related to urban resilience by visualizing spatially the output of the dynamic model in a final map and therefore, identifying specific policies and solutions. • Scenario planning refers to the prediction of future scenarios and the definition for each scenario of objectives and strategies. Both SDM and LV models allow to predict the way variables evolve, starting from the state of art conditions (t0) [50]. In this sense, both the SDM and the LV models are useful supports for the decision makers for identifying the most critical areas and adopting specific policies and interventions.
• Scale refers to the application of dynamic models at different scales. Moreover, the SDM considers a system as a whole, analyzing and focusing on its components and sub-components.
In fact, SDMs are mostly applied to municipal or metropolitan scales. LV models are generally employed to provincial and sub-regional scales and to those territories with a rural vocation.

•
Mapping is intended as the possibility to visualize the scenarios using GIS-based methods and the possibility to interact the dynamic model and the GIS interface through a programming language (e.g., QGIS and Python). Actually, the integration of DMs simulation results into GIS is developed by users in specific plug-ins (e.g., PANDORA 3.0 [97]) or by using specific coding platforms (e.g., QGIS Python console) and to get a spatial visualization of the output. Despite the requirement of specific competences to manage DMs in GIS environment, the users may support decision makers in better interpreting certain dynamics related to urban resilience by visualizing spatially the output of the dynamic model in a final map and therefore, identifying specific policies and solutions. • Scenario planning refers to the prediction of future scenarios and the definition for each scenario of objectives and strategies. Both SDM and LV models allow to predict the way variables evolve, starting from the state of art conditions (t0) [50]. In this sense, both the SDM and the LV models are useful supports for the decision makers for identifying the most critical areas and adopting specific policies and interventions.
• Scale refers to the application of dynamic models at different scales. Moreover, the SDM considers a system as a whole, analyzing and focusing on its components and sub-components.
In fact, SDMs are mostly applied to municipal or metropolitan scales. LV models are generally employed to provincial and sub-regional scales and to those territories with a rural vocation. al. [96] integrate SDM and Agent-Based Models to better understand the effects, not only on the system but also on the agent of the transition to sustainable mobility.

•
Mapping is intended as the possibility to visualize the scenarios using GIS-based methods and the possibility to interact the dynamic model and the GIS interface through a programming language (e.g., QGIS and Python). Actually, the integration of DMs simulation results into GIS is developed by users in specific plug-ins (e.g., PANDORA 3.0 [97]) or by using specific coding platforms (e.g., QGIS Python console) and to get a spatial visualization of the output. Despite the requirement of specific competences to manage DMs in GIS environment, the users may support decision makers in better interpreting certain dynamics related to urban resilience by visualizing spatially the output of the dynamic model in a final map and therefore, identifying specific policies and solutions. • Scenario planning refers to the prediction of future scenarios and the definition for each scenario of objectives and strategies. Both SDM and LV models allow to predict the way variables evolve, starting from the state of art conditions (t0) [50]. In this sense, both the SDM and the LV models are useful supports for the decision makers for identifying the most critical areas and adopting specific policies and interventions.
• Scale refers to the application of dynamic models at different scales. Moreover, the SDM considers a system as a whole, analyzing and focusing on its components and sub-components.
In fact, SDMs are mostly applied to municipal or metropolitan scales. LV models are generally employed to provincial and sub-regional scales and to those territories with a rural vocation. al. [96] integrate SDM and Agent-Based Models to better understand the effects, not only on the system but also on the agent of the transition to sustainable mobility.

•
Mapping is intended as the possibility to visualize the scenarios using GIS-based methods and the possibility to interact the dynamic model and the GIS interface through a programming language (e.g., QGIS and Python). Actually, the integration of DMs simulation results into GIS is developed by users in specific plug-ins (e.g., PANDORA 3.0 [97]) or by using specific coding platforms (e.g., QGIS Python console) and to get a spatial visualization of the output. Despite the requirement of specific competences to manage DMs in GIS environment, the users may support decision makers in better interpreting certain dynamics related to urban resilience by visualizing spatially the output of the dynamic model in a final map and therefore, identifying specific policies and solutions.

•
Scenario planning refers to the prediction of future scenarios and the definition for each scenario of objectives and strategies. Both SDM and LV models allow to predict the way variables evolve, starting from the state of art conditions (t0) [50]. In this sense, both the SDM and the LV models are useful supports for the decision makers for identifying the most critical areas and adopting specific policies and interventions.
• Scale refers to the application of dynamic models at different scales. Moreover, the SDM considers a system as a whole, analyzing and focusing on its components and sub-components.
In fact, SDMs are mostly applied to municipal or metropolitan scales. LV models are generally employed to provincial and sub-regional scales and to those territories with a rural vocation.

Nature
Essence and characters *

Input
Use of qualitative and quantitative data Participatory process Use of different spatial scales

Scenario simulation
Time scale Graphical representation the possibility to interact the dynamic model and the GIS interface through a programming language (e.g., QGIS and Python). Actually, the integration of DMs simulation results into GIS is developed by users in specific plug-ins (e.g., PANDORA 3.0 [97]) or by using specific coding platforms (e.g., QGIS Python console) and to get a spatial visualization of the output. Despite the requirement of specific competences to manage DMs in GIS environment, the users may support decision makers in better interpreting certain dynamics related to urban resilience by visualizing spatially the output of the dynamic model in a final map and therefore, identifying specific policies and solutions. • Scenario planning refers to the prediction of future scenarios and the definition for each scenario of objectives and strategies. Both SDM and LV models allow to predict the way variables evolve, starting from the state of art conditions (t0) [50]. In this sense, both the SDM and the LV models are useful supports for the decision makers for identifying the most critical areas and adopting specific policies and interventions.
• Scale refers to the application of dynamic models at different scales. Moreover, the SDM considers a system as a whole, analyzing and focusing on its components and sub-components.
In fact, SDMs are mostly applied to municipal or metropolitan scales. LV models are generally employed to provincial and sub-regional scales and to those territories with a rural vocation. phases: (1) at the beginning, to support the problem articulation and the identification of the variables to be included in the model; (2) after the scenarios' simulation to support the evaluation of the different performances through final score calculation or ranking elaboration. Shafiei et al. [96] integrate SDM and Agent-Based Models to better understand the effects, not only on the system but also on the agent of the transition to sustainable mobility.

•
Mapping is intended as the possibility to visualize the scenarios using GIS-based methods and the possibility to interact the dynamic model and the GIS interface through a programming language (e.g., QGIS and Python). Actually, the integration of DMs simulation results into GIS is developed by users in specific plug-ins (e.g., PANDORA 3.0 [97]) or by using specific coding platforms (e.g., QGIS Python console) and to get a spatial visualization of the output. Despite the requirement of specific competences to manage DMs in GIS environment, the users may support decision makers in better interpreting certain dynamics related to urban resilience by visualizing spatially the output of the dynamic model in a final map and therefore, identifying specific policies and solutions.

•
Scenario planning refers to the prediction of future scenarios and the definition for each scenario of objectives and strategies. Both SDM and LV models allow to predict the way variables evolve, starting from the state of art conditions (t0) [50]. In this sense, both the SDM and the LV models are useful supports for the decision makers for identifying the most critical areas and adopting specific policies and interventions.
• Scale refers to the application of dynamic models at different scales. Moreover, the SDM considers a system as a whole, analyzing and focusing on its components and sub-components.
In fact, SDMs are mostly applied to municipal or metropolitan scales. LV models are generally employed to provincial and sub-regional scales and to those territories with a rural vocation.

System Dynamic Models
Nature Essence and characters *

Input
Use of qualitative and quantitative data Participatory process Use of different spatial scales

Scenario simulation
Time scale

Sensitivity analysis
system but also on the agent of the transition to sustainable mobility.

•
Mapping is intended as the possibility to visualize the scenarios using GIS-based methods and the possibility to interact the dynamic model and the GIS interface through a programming language (e.g., QGIS and Python). Actually, the integration of DMs simulation results into GIS is developed by users in specific plug-ins (e.g., PANDORA 3.0 [97]) or by using specific coding platforms (e.g., QGIS Python console) and to get a spatial visualization of the output. Despite the requirement of specific competences to manage DMs in GIS environment, the users may support decision makers in better interpreting certain dynamics related to urban resilience by visualizing spatially the output of the dynamic model in a final map and therefore, identifying specific policies and solutions. • Scenario planning refers to the prediction of future scenarios and the definition for each scenario of objectives and strategies. Both SDM and LV models allow to predict the way variables evolve, starting from the state of art conditions (t0) [50]. In this sense, both the SDM and the LV models are useful supports for the decision makers for identifying the most critical areas and adopting specific policies and interventions.
• Scale refers to the application of dynamic models at different scales. Moreover, the SDM considers a system as a whole, analyzing and focusing on its components and sub-components.
In fact, SDMs are mostly applied to municipal or metropolitan scales. LV models are generally employed to provincial and sub-regional scales and to those territories with a rural vocation.

Nature
Essence and characters *

Input
Use of qualitative and quantitative data Participatory process Use of different spatial scales

Scenario simulation
Time scale integrated with Multicriteria Analysis (MCA) [75], as well as with the Agent-Based Models (ABM) [94] and Hedonic Price Model (HPM) [95]. Specifically, MCA can be used at two different phases: (1) at the beginning, to support the problem articulation and the identification of the variables to be included in the model; (2) after the scenarios' simulation to support the evaluation of the different performances through final score calculation or ranking elaboration. Shafiei et al. [96] integrate SDM and Agent-Based Models to better understand the effects, not only on the system but also on the agent of the transition to sustainable mobility.

•
Mapping is intended as the possibility to visualize the scenarios using GIS-based methods and the possibility to interact the dynamic model and the GIS interface through a programming language (e.g., QGIS and Python). Actually, the integration of DMs simulation results into GIS is developed by users in specific plug-ins (e.g., PANDORA 3.0 [97]) or by using specific coding platforms (e.g., QGIS Python console) and to get a spatial visualization of the output. Despite the requirement of specific competences to manage DMs in GIS environment, the users may support decision makers in better interpreting certain dynamics related to urban resilience by visualizing spatially the output of the dynamic model in a final map and therefore, identifying specific policies and solutions.

•
Scenario planning refers to the prediction of future scenarios and the definition for each scenario of objectives and strategies. Both SDM and LV models allow to predict the way variables evolve, starting from the state of art conditions (t0) [50]. In this sense, both the SDM and the LV models are useful supports for the decision makers for identifying the most critical areas and adopting specific policies and interventions.
• Scale refers to the application of dynamic models at different scales. Moreover, the SDM considers a system as a whole, analyzing and focusing on its components and sub-components.
In fact, SDMs are mostly applied to municipal or metropolitan scales. LV models are generally employed to provincial and sub-regional scales and to those territories with a rural vocation.

Nature
Essence and characters *

Input
Use of qualitative and quantitative data Participatory process

Scenario simulation
Time scale

Availability
• Integration refers to the capability of DMs to integrate different techniques and evaluation methodologies. For instance, the considered dynamic models are a suitable tool to being integrated with Multicriteria Analysis (MCA) [75], as well as with the Agent-Based Models (ABM) [94] and Hedonic Price Model (HPM) [95]. Specifically, MCA can be used at two different phases: (1) at the beginning, to support the problem articulation and the identification of the variables to be included in the model; (2) after the scenarios' simulation to support the evaluation of the different performances through final score calculation or ranking elaboration. Shafiei et al. [96] integrate SDM and Agent-Based Models to better understand the effects, not only on the system but also on the agent of the transition to sustainable mobility.

•
Mapping is intended as the possibility to visualize the scenarios using GIS-based methods and the possibility to interact the dynamic model and the GIS interface through a programming language (e.g., QGIS and Python). Actually, the integration of DMs simulation results into GIS is developed by users in specific plug-ins (e.g., PANDORA 3.0 [97]) or by using specific coding platforms (e.g., QGIS Python console) and to get a spatial visualization of the output. Despite the requirement of specific competences to manage DMs in GIS environment, the users may support decision makers in better interpreting certain dynamics related to urban resilience by visualizing spatially the output of the dynamic model in a final map and therefore, identifying specific policies and solutions. • Scenario planning refers to the prediction of future scenarios and the definition for each scenario of objectives and strategies. Both SDM and LV models allow to predict the way variables evolve, starting from the state of art conditions (t0) [50]. In this sense, both the SDM and the LV models are useful supports for the decision makers for identifying the most critical areas and adopting specific policies and interventions.
• Scale refers to the application of dynamic models at different scales. Moreover, the SDM considers a system as a whole, analyzing and focusing on its components and sub-components.
In fact, SDMs are mostly applied to municipal or metropolitan scales. LV models are generally employed to provincial and sub-regional scales and to those territories with a rural vocation.

Nature
Essence and characters *

Input
Use of qualitative and quantitative data Participatory process

Scenario simulation
Time scale • Integration refers to the capability of DMs to integrate different techniques and evaluation methodologies. For instance, the considered dynamic models are a suitable tool to being integrated with Multicriteria Analysis (MCA) [75], as well as with the Agent-Based Models (ABM) [94] and Hedonic Price Model (HPM) [95]. Specifically, MCA can be used at two different phases: (1) at the beginning, to support the problem articulation and the identification of the variables to be included in the model; (2) after the scenarios' simulation to support the evaluation of the different performances through final score calculation or ranking elaboration. Shafiei et al. [96] integrate SDM and Agent-Based Models to better understand the effects, not only on the system but also on the agent of the transition to sustainable mobility.

•
Mapping is intended as the possibility to visualize the scenarios using GIS-based methods and the possibility to interact the dynamic model and the GIS interface through a programming language (e.g., QGIS and Python). Actually, the integration of DMs simulation results into GIS is developed by users in specific plug-ins (e.g., PANDORA 3.0 [97]) or by using specific coding platforms (e.g., QGIS Python console) and to get a spatial visualization of the output. Despite the requirement of specific competences to manage DMs in GIS environment, the users may support decision makers in better interpreting certain dynamics related to urban resilience by visualizing spatially the output of the dynamic model in a final map and therefore, identifying specific policies and solutions. • Scenario planning refers to the prediction of future scenarios and the definition for each scenario of objectives and strategies. Both SDM and LV models allow to predict the way variables evolve, starting from the state of art conditions (t0) [50]. In this sense, both the SDM and the LV models are useful supports for the decision makers for identifying the most critical areas and adopting specific policies and interventions.
• Scale refers to the application of dynamic models at different scales. Moreover, the SDM considers a system as a whole, analyzing and focusing on its components and sub-components.
In fact, SDMs are mostly applied to municipal or metropolitan scales. LV models are generally employed to provincial and sub-regional scales and to those territories with a rural vocation.

Nature
Essence and characters *

Input
Use of qualitative and quantitative data Participatory process

Scenario simulation
Time scale

Use of Ordinary Differential Equations
open programming languages, such "deSolve" for R, "Simupy" for Python, "Mat Cont for Matlab" and "Nova modeler" for ecological modelling. • Integration refers to the capability of DMs to integrate different techniques and evaluation methodologies. For instance, the considered dynamic models are a suitable tool to being integrated with Multicriteria Analysis (MCA) [75], as well as with the Agent-Based Models (ABM) [94] and Hedonic Price Model (HPM) [95]. Specifically, MCA can be used at two different phases: (1) at the beginning, to support the problem articulation and the identification of the variables to be included in the model; (2) after the scenarios' simulation to support the evaluation of the different performances through final score calculation or ranking elaboration. Shafiei et al. [96] integrate SDM and Agent-Based Models to better understand the effects, not only on the system but also on the agent of the transition to sustainable mobility.

•
Mapping is intended as the possibility to visualize the scenarios using GIS-based methods and the possibility to interact the dynamic model and the GIS interface through a programming language (e.g., QGIS and Python). Actually, the integration of DMs simulation results into GIS is developed by users in specific plug-ins (e.g., PANDORA 3.0 [97]) or by using specific coding platforms (e.g., QGIS Python console) and to get a spatial visualization of the output. Despite the requirement of specific competences to manage DMs in GIS environment, the users may support decision makers in better interpreting certain dynamics related to urban resilience by visualizing spatially the output of the dynamic model in a final map and therefore, identifying specific policies and solutions. • Scenario planning refers to the prediction of future scenarios and the definition for each scenario of objectives and strategies. Both SDM and LV models allow to predict the way variables evolve, starting from the state of art conditions (t0) [50]. In this sense, both the SDM and the LV models are useful supports for the decision makers for identifying the most critical areas and adopting specific policies and interventions.
• Scale refers to the application of dynamic models at different scales. Moreover, the SDM considers a system as a whole, analyzing and focusing on its components and sub-components.
In fact, SDMs are mostly applied to municipal or metropolitan scales. LV models are generally employed to provincial and sub-regional scales and to those territories with a rural vocation.

Nature
Essence and characters *

Input
Use of qualitative and quantitative data Participatory process

Scenario simulation
Time scale open programming languages, such "deSolve" for R, "Simupy" for Python, "Mat Cont for Matlab" and "Nova modeler" for ecological modelling. • Integration refers to the capability of DMs to integrate different techniques and evaluation methodologies. For instance, the considered dynamic models are a suitable tool to being integrated with Multicriteria Analysis (MCA) [75], as well as with the Agent-Based Models (ABM) [94] and Hedonic Price Model (HPM) [95]. Specifically, MCA can be used at two different phases: (1) at the beginning, to support the problem articulation and the identification of the variables to be included in the model; (2) after the scenarios' simulation to support the evaluation of the different performances through final score calculation or ranking elaboration. Shafiei et al. [96] integrate SDM and Agent-Based Models to better understand the effects, not only on the system but also on the agent of the transition to sustainable mobility.

•
Mapping is intended as the possibility to visualize the scenarios using GIS-based methods and the possibility to interact the dynamic model and the GIS interface through a programming language (e.g., QGIS and Python). Actually, the integration of DMs simulation results into GIS is developed by users in specific plug-ins (e.g., PANDORA 3.0 [97]) or by using specific coding platforms (e.g., QGIS Python console) and to get a spatial visualization of the output. Despite the requirement of specific competences to manage DMs in GIS environment, the users may support decision makers in better interpreting certain dynamics related to urban resilience by visualizing spatially the output of the dynamic model in a final map and therefore, identifying specific policies and solutions. • Scenario planning refers to the prediction of future scenarios and the definition for each scenario of objectives and strategies. Both SDM and LV models allow to predict the way variables evolve, starting from the state of art conditions (t0) [50]. In this sense, both the SDM and the LV models are useful supports for the decision makers for identifying the most critical areas and adopting specific policies and interventions.
• Scale refers to the application of dynamic models at different scales. Moreover, the SDM considers a system as a whole, analyzing and focusing on its components and sub-components.
In fact, SDMs are mostly applied to municipal or metropolitan scales. LV models are generally employed to provincial and sub-regional scales and to those territories with a rural vocation.

Nature
Essence and characters *

Input
Use of qualitative and quantitative data Participatory process Use of different spatial scales

Scenario simulation
Time scale

Integration
Integration with different techniques and methodologies these need to write manually the ODEs to obtain the prediction of scenarios ( Figure 6). In this sense, both the dynamic models use the ODEs as an output, but in different ways. From the point of view of the availability, both dynamic models may be written through specific packages in open programming languages, such "deSolve" for R, "Simupy" for Python, "Mat Cont for Matlab" and "Nova modeler" for ecological modelling.

•
Integration refers to the capability of DMs to integrate different techniques and evaluation methodologies. For instance, the considered dynamic models are a suitable tool to being integrated with Multicriteria Analysis (MCA) [75], as well as with the Agent-Based Models (ABM) [94] and Hedonic Price Model (HPM) [95]. Specifically, MCA can be used at two different phases: (1) at the beginning, to support the problem articulation and the identification of the variables to be included in the model; (2) after the scenarios' simulation to support the evaluation of the different performances through final score calculation or ranking elaboration. Shafiei et al. [96] integrate SDM and Agent-Based Models to better understand the effects, not only on the system but also on the agent of the transition to sustainable mobility.

•
Mapping is intended as the possibility to visualize the scenarios using GIS-based methods and the possibility to interact the dynamic model and the GIS interface through a programming language (e.g., QGIS and Python). Actually, the integration of DMs simulation results into GIS is developed by users in specific plug-ins (e.g., PANDORA 3.0 [97]) or by using specific coding platforms (e.g., QGIS Python console) and to get a spatial visualization of the output. Despite the requirement of specific competences to manage DMs in GIS environment, the users may support decision makers in better interpreting certain dynamics related to urban resilience by visualizing spatially the output of the dynamic model in a final map and therefore, identifying specific policies and solutions.

•
Scenario planning refers to the prediction of future scenarios and the definition for each scenario of objectives and strategies. Both SDM and LV models allow to predict the way variables evolve, starting from the state of art conditions (t0) [50]. In this sense, both the SDM and the LV models are useful supports for the decision makers for identifying the most critical areas and adopting specific policies and interventions.
• Scale refers to the application of dynamic models at different scales. Moreover, the SDM considers a system as a whole, analyzing and focusing on its components and sub-components.
In fact, SDMs are mostly applied to municipal or metropolitan scales. LV models are generally employed to provincial and sub-regional scales and to those territories with a rural vocation.

Nature
Essence and characters *

Input
Use of qualitative and quantitative data Participatory process Use of different spatial scales

Scenario simulation
Time scale these need to write manually the ODEs to obtain the prediction of scenarios ( Figure 6). In this sense, both the dynamic models use the ODEs as an output, but in different ways. From the point of view of the availability, both dynamic models may be written through specific packages in open programming languages, such "deSolve" for R, "Simupy" for Python, "Mat Cont for Matlab" and "Nova modeler" for ecological modelling.

•
Integration refers to the capability of DMs to integrate different techniques and evaluation methodologies. For instance, the considered dynamic models are a suitable tool to being integrated with Multicriteria Analysis (MCA) [75], as well as with the Agent-Based Models (ABM) [94] and Hedonic Price Model (HPM) [95]. Specifically, MCA can be used at two different phases: (1) at the beginning, to support the problem articulation and the identification of the variables to be included in the model; (2) after the scenarios' simulation to support the evaluation of the different performances through final score calculation or ranking elaboration. Shafiei et al. [96] integrate SDM and Agent-Based Models to better understand the effects, not only on the system but also on the agent of the transition to sustainable mobility.

•
Mapping is intended as the possibility to visualize the scenarios using GIS-based methods and the possibility to interact the dynamic model and the GIS interface through a programming language (e.g., QGIS and Python). Actually, the integration of DMs simulation results into GIS is developed by users in specific plug-ins (e.g., PANDORA 3.0 [97]) or by using specific coding platforms (e.g., QGIS Python console) and to get a spatial visualization of the output. Despite the requirement of specific competences to manage DMs in GIS environment, the users may support decision makers in better interpreting certain dynamics related to urban resilience by visualizing spatially the output of the dynamic model in a final map and therefore, identifying specific policies and solutions.

•
Scenario planning refers to the prediction of future scenarios and the definition for each scenario of objectives and strategies. Both SDM and LV models allow to predict the way variables evolve, starting from the state of art conditions (t0) [50]. In this sense, both the SDM and the LV models are useful supports for the decision makers for identifying the most critical areas and adopting specific policies and interventions.
• Scale refers to the application of dynamic models at different scales. Moreover, the SDM considers a system as a whole, analyzing and focusing on its components and sub-components.
In fact, SDMs are mostly applied to municipal or metropolitan scales. LV models are generally employed to provincial and sub-regional scales and to those territories with a rural vocation.

Nature
Essence and characters *

Input
Use of qualitative and quantitative data Participatory process Use of different spatial scales

Scenario simulation
Time scale

GIS visualization
these need to write manually the ODEs to obtain the prediction of scenarios ( Figure 6). In this sense, both the dynamic models use the ODEs as an output, but in different ways. From the point of view of the availability, both dynamic models may be written through specific packages in open programming languages, such "deSolve" for R, "Simupy" for Python, "Mat Cont for Matlab" and "Nova modeler" for ecological modelling.

•
Integration refers to the capability of DMs to integrate different techniques and evaluation methodologies. For instance, the considered dynamic models are a suitable tool to being integrated with Multicriteria Analysis (MCA) [75], as well as with the Agent-Based Models (ABM) [94] and Hedonic Price Model (HPM) [95]. Specifically, MCA can be used at two different phases: (1) at the beginning, to support the problem articulation and the identification of the variables to be included in the model; (2) after the scenarios' simulation to support the evaluation of the different performances through final score calculation or ranking elaboration. Shafiei et al. [96] integrate SDM and Agent-Based Models to better understand the effects, not only on the system but also on the agent of the transition to sustainable mobility.

•
Mapping is intended as the possibility to visualize the scenarios using GIS-based methods and the possibility to interact the dynamic model and the GIS interface through a programming language (e.g., QGIS and Python). Actually, the integration of DMs simulation results into GIS is developed by users in specific plug-ins (e.g., PANDORA 3.0 [97]) or by using specific coding platforms (e.g., QGIS Python console) and to get a spatial visualization of the output. Despite the requirement of specific competences to manage DMs in GIS environment, the users may support decision makers in better interpreting certain dynamics related to urban resilience by visualizing spatially the output of the dynamic model in a final map and therefore, identifying specific policies and solutions.

•
Scenario planning refers to the prediction of future scenarios and the definition for each scenario of objectives and strategies. Both SDM and LV models allow to predict the way variables evolve, starting from the state of art conditions (t0) [50]. In this sense, both the SDM and the LV models are useful supports for the decision makers for identifying the most critical areas and adopting specific policies and interventions.
• Scale refers to the application of dynamic models at different scales. Moreover, the SDM considers a system as a whole, analyzing and focusing on its components and sub-components.
In fact, SDMs are mostly applied to municipal or metropolitan scales. LV models are generally employed to provincial and sub-regional scales and to those territories with a rural vocation.

Lotka-Volterra Models System Dynamic Models Nature
Essence and characters *

Input
Use of qualitative and quantitative data Participatory process Use of different spatial scales

Scenario simulation
Time scale these need to write manually the ODEs to obtain the prediction of scenarios ( Figure 6). In this sense, both the dynamic models use the ODEs as an output, but in different ways. From the point of view of the availability, both dynamic models may be written through specific packages in open programming languages, such "deSolve" for R, "Simupy" for Python, "Mat Cont for Matlab" and "Nova modeler" for ecological modelling.
• Integration refers to the capability of DMs to integrate different techniques and evaluation methodologies. For instance, the considered dynamic models are a suitable tool to being integrated with Multicriteria Analysis (MCA) [75], as well as with the Agent-Based Models (ABM) [94] and Hedonic Price Model (HPM) [95]. Specifically, MCA can be used at two different phases: (1) at the beginning, to support the problem articulation and the identification of the variables to be included in the model; (2) after the scenarios' simulation to support the evaluation of the different performances through final score calculation or ranking elaboration. Shafiei et al. [96] integrate SDM and Agent-Based Models to better understand the effects, not only on the system but also on the agent of the transition to sustainable mobility.

•
Mapping is intended as the possibility to visualize the scenarios using GIS-based methods and the possibility to interact the dynamic model and the GIS interface through a programming language (e.g., QGIS and Python). Actually, the integration of DMs simulation results into GIS is developed by users in specific plug-ins (e.g., PANDORA 3.0 [97]) or by using specific coding platforms (e.g., QGIS Python console) and to get a spatial visualization of the output. Despite the requirement of specific competences to manage DMs in GIS environment, the users may support decision makers in better interpreting certain dynamics related to urban resilience by visualizing spatially the output of the dynamic model in a final map and therefore, identifying specific policies and solutions.

•
Scenario planning refers to the prediction of future scenarios and the definition for each scenario of objectives and strategies. Both SDM and LV models allow to predict the way variables evolve, starting from the state of art conditions (t0) [50]. In this sense, both the SDM and the LV models are useful supports for the decision makers for identifying the most critical areas and adopting specific policies and interventions.
• Scale refers to the application of dynamic models at different scales. Moreover, the SDM considers a system as a whole, analyzing and focusing on its components and sub-components.
In fact, SDMs are mostly applied to municipal or metropolitan scales. LV models are generally employed to provincial and sub-regional scales and to those territories with a rural vocation.

Lotka-Volterra Models System Dynamic Models Nature
Essence and characters *

Input
Use of qualitative and quantitative data Participatory process Use of different spatial scales

Time scale
Interactivity of view of the availability, both dynamic models may be written through specific packages in open programming languages, such "deSolve" for R, "Simupy" for Python, "Mat Cont for Matlab" and "Nova modeler" for ecological modelling.
• Integration refers to the capability of DMs to integrate different techniques and evaluation methodologies. For instance, the considered dynamic models are a suitable tool to being integrated with Multicriteria Analysis (MCA) [75], as well as with the Agent-Based Models (ABM) [94] and Hedonic Price Model (HPM) [95]. Specifically, MCA can be used at two different phases: (1) at the beginning, to support the problem articulation and the identification of the variables to be included in the model; (2) after the scenarios' simulation to support the evaluation of the different performances through final score calculation or ranking elaboration. Shafiei et al. [96] integrate SDM and Agent-Based Models to better understand the effects, not only on the system but also on the agent of the transition to sustainable mobility.

•
Mapping is intended as the possibility to visualize the scenarios using GIS-based methods and the possibility to interact the dynamic model and the GIS interface through a programming language (e.g., QGIS and Python). Actually, the integration of DMs simulation results into GIS is developed by users in specific plug-ins (e.g., PANDORA 3.0 [97]) or by using specific coding platforms (e.g., QGIS Python console) and to get a spatial visualization of the output. Despite the requirement of specific competences to manage DMs in GIS environment, the users may support decision makers in better interpreting certain dynamics related to urban resilience by visualizing spatially the output of the dynamic model in a final map and therefore, identifying specific policies and solutions.

•
Scenario planning refers to the prediction of future scenarios and the definition for each scenario of objectives and strategies. Both SDM and LV models allow to predict the way variables evolve, starting from the state of art conditions (t0) [50]. In this sense, both the SDM and the LV models are useful supports for the decision makers for identifying the most critical areas and adopting specific policies and interventions.
• Scale refers to the application of dynamic models at different scales. Moreover, the SDM considers a system as a whole, analyzing and focusing on its components and sub-components.
In fact, SDMs are mostly applied to municipal or metropolitan scales. LV models are generally employed to provincial and sub-regional scales and to those territories with a rural vocation. Table 6. Lotka-Volterra models and System Dynamic Models: summarizing comparison matrix (Authors' elaboration, 2019).

Nature
Essence and characters *

Input
Use of qualitative and quantitative data Participatory process Use of different spatial scales

Scenario simulation
Time scale of view of the availability, both dynamic models may be written through specific packages in open programming languages, such "deSolve" for R, "Simupy" for Python, "Mat Cont for Matlab" and "Nova modeler" for ecological modelling.

•
Integration refers to the capability of DMs to integrate different techniques and evaluation methodologies. For instance, the considered dynamic models are a suitable tool to being integrated with Multicriteria Analysis (MCA) [75], as well as with the Agent-Based Models (ABM) [94] and Hedonic Price Model (HPM) [95]. Specifically, MCA can be used at two different phases: (1) at the beginning, to support the problem articulation and the identification of the variables to be included in the model; (2) after the scenarios' simulation to support the evaluation of the different performances through final score calculation or ranking elaboration. Shafiei et al. [96] integrate SDM and Agent-Based Models to better understand the effects, not only on the system but also on the agent of the transition to sustainable mobility.

•
Mapping is intended as the possibility to visualize the scenarios using GIS-based methods and the possibility to interact the dynamic model and the GIS interface through a programming language (e.g., QGIS and Python). Actually, the integration of DMs simulation results into GIS is developed by users in specific plug-ins (e.g., PANDORA 3.0 [97]) or by using specific coding platforms (e.g., QGIS Python console) and to get a spatial visualization of the output. Despite the requirement of specific competences to manage DMs in GIS environment, the users may support decision makers in better interpreting certain dynamics related to urban resilience by visualizing spatially the output of the dynamic model in a final map and therefore, identifying specific policies and solutions.

•
Scenario planning refers to the prediction of future scenarios and the definition for each scenario of objectives and strategies. Both SDM and LV models allow to predict the way variables evolve, starting from the state of art conditions (t0) [50]. In this sense, both the SDM and the LV models are useful supports for the decision makers for identifying the most critical areas and adopting specific policies and interventions.
• Scale refers to the application of dynamic models at different scales. Moreover, the SDM considers a system as a whole, analyzing and focusing on its components and sub-components.
In fact, SDMs are mostly applied to municipal or metropolitan scales. LV models are generally employed to provincial and sub-regional scales and to those territories with a rural vocation. Table 6. Lotka-Volterra models and System Dynamic Models: summarizing comparison matrix (Authors' elaboration, 2019).

Nature
Essence and characters *

Input
Use of qualitative and quantitative data Participatory process Use of different spatial scales

Scenario simulation
Time scale

Scenario planning
Definition of objectives and strategies specific software, such as STELLA, Venism and Powerism, that formulate themselves the ODEs from which the scenarios' simulations are produced. On the other hand, LV models are generally employed through mathematical software, such as MatLab and Mathematica Software, and these need to write manually the ODEs to obtain the prediction of scenarios ( Figure 6). In this sense, both the dynamic models use the ODEs as an output, but in different ways. From the point of view of the availability, both dynamic models may be written through specific packages in open programming languages, such "deSolve" for R, "Simupy" for Python, "Mat Cont for Matlab" and "Nova modeler" for ecological modelling.

•
Integration refers to the capability of DMs to integrate different techniques and evaluation methodologies. For instance, the considered dynamic models are a suitable tool to being integrated with Multicriteria Analysis (MCA) [75], as well as with the Agent-Based Models (ABM) [94] and Hedonic Price Model (HPM) [95]. Specifically, MCA can be used at two different phases: (1) at the beginning, to support the problem articulation and the identification of the variables to be included in the model; (2) after the scenarios' simulation to support the evaluation of the different performances through final score calculation or ranking elaboration. Shafiei et al. [96] integrate SDM and Agent-Based Models to better understand the effects, not only on the system but also on the agent of the transition to sustainable mobility.

•
Mapping is intended as the possibility to visualize the scenarios using GIS-based methods and the possibility to interact the dynamic model and the GIS interface through a programming language (e.g., QGIS and Python). Actually, the integration of DMs simulation results into GIS is developed by users in specific plug-ins (e.g., PANDORA 3.0 [97]) or by using specific coding platforms (e.g., QGIS Python console) and to get a spatial visualization of the output. Despite the requirement of specific competences to manage DMs in GIS environment, the users may support decision makers in better interpreting certain dynamics related to urban resilience by visualizing spatially the output of the dynamic model in a final map and therefore, identifying specific policies and solutions.

•
Scenario planning refers to the prediction of future scenarios and the definition for each scenario of objectives and strategies. Both SDM and LV models allow to predict the way variables evolve, starting from the state of art conditions (t0) [50]. In this sense, both the SDM and the LV models are useful supports for the decision makers for identifying the most critical areas and adopting specific policies and interventions.
• Scale refers to the application of dynamic models at different scales. Moreover, the SDM considers a system as a whole, analyzing and focusing on its components and sub-components.
In fact, SDMs are mostly applied to municipal or metropolitan scales. LV models are generally employed to provincial and sub-regional scales and to those territories with a rural vocation. specific software, such as STELLA, Venism and Powerism, that formulate themselves the ODEs from which the scenarios' simulations are produced. On the other hand, LV models are generally employed through mathematical software, such as MatLab and Mathematica Software, and these need to write manually the ODEs to obtain the prediction of scenarios ( Figure 6). In this sense, both the dynamic models use the ODEs as an output, but in different ways. From the point of view of the availability, both dynamic models may be written through specific packages in open programming languages, such "deSolve" for R, "Simupy" for Python, "Mat Cont for Matlab" and "Nova modeler" for ecological modelling.

•
Integration refers to the capability of DMs to integrate different techniques and evaluation methodologies. For instance, the considered dynamic models are a suitable tool to being integrated with Multicriteria Analysis (MCA) [75], as well as with the Agent-Based Models (ABM) [94] and Hedonic Price Model (HPM) [95]. Specifically, MCA can be used at two different phases: (1) at the beginning, to support the problem articulation and the identification of the variables to be included in the model; (2) after the scenarios' simulation to support the evaluation of the different performances through final score calculation or ranking elaboration. Shafiei et al. [96] integrate SDM and Agent-Based Models to better understand the effects, not only on the system but also on the agent of the transition to sustainable mobility.

•
Mapping is intended as the possibility to visualize the scenarios using GIS-based methods and the possibility to interact the dynamic model and the GIS interface through a programming language (e.g., QGIS and Python). Actually, the integration of DMs simulation results into GIS is developed by users in specific plug-ins (e.g., PANDORA 3.0 [97]) or by using specific coding platforms (e.g., QGIS Python console) and to get a spatial visualization of the output. Despite the requirement of specific competences to manage DMs in GIS environment, the users may support decision makers in better interpreting certain dynamics related to urban resilience by visualizing spatially the output of the dynamic model in a final map and therefore, identifying specific policies and solutions.

•
Scenario planning refers to the prediction of future scenarios and the definition for each scenario of objectives and strategies. Both SDM and LV models allow to predict the way variables evolve, starting from the state of art conditions (t0) [50]. In this sense, both the SDM and the LV models are useful supports for the decision makers for identifying the most critical areas and adopting specific policies and interventions.
• Scale refers to the application of dynamic models at different scales. Moreover, the SDM considers a system as a whole, analyzing and focusing on its components and sub-components.
In fact, SDMs are mostly applied to municipal or metropolitan scales. LV models are generally employed to provincial and sub-regional scales and to those territories with a rural vocation. specific software, such as STELLA, Venism and Powerism, that formulate themselves the ODEs from which the scenarios' simulations are produced. On the other hand, LV models are generally employed through mathematical software, such as MatLab and Mathematica Software, and these need to write manually the ODEs to obtain the prediction of scenarios ( Figure 6). In this sense, both the dynamic models use the ODEs as an output, but in different ways. From the point of view of the availability, both dynamic models may be written through specific packages in open programming languages, such "deSolve" for R, "Simupy" for Python, "Mat Cont for Matlab" and "Nova modeler" for ecological modelling.

•
Integration refers to the capability of DMs to integrate different techniques and evaluation methodologies. For instance, the considered dynamic models are a suitable tool to being integrated with Multicriteria Analysis (MCA) [75], as well as with the Agent-Based Models (ABM) [94] and Hedonic Price Model (HPM) [95]. Specifically, MCA can be used at two different phases: (1) at the beginning, to support the problem articulation and the identification of the variables to be included in the model; (2) after the scenarios' simulation to support the evaluation of the different performances through final score calculation or ranking elaboration. Shafiei et al. [96] integrate SDM and Agent-Based Models to better understand the effects, not only on the system but also on the agent of the transition to sustainable mobility.

•
Mapping is intended as the possibility to visualize the scenarios using GIS-based methods and the possibility to interact the dynamic model and the GIS interface through a programming language (e.g., QGIS and Python). Actually, the integration of DMs simulation results into GIS is developed by users in specific plug-ins (e.g., PANDORA 3.0 [97]) or by using specific coding platforms (e.g., QGIS Python console) and to get a spatial visualization of the output. Despite the requirement of specific competences to manage DMs in GIS environment, the users may support decision makers in better interpreting certain dynamics related to urban resilience by visualizing spatially the output of the dynamic model in a final map and therefore, identifying specific policies and solutions.

•
Scenario planning refers to the prediction of future scenarios and the definition for each scenario of objectives and strategies. Both SDM and LV models allow to predict the way variables evolve, starting from the state of art conditions (t0) [50]. In this sense, both the SDM and the LV models are useful supports for the decision makers for identifying the most critical areas and adopting specific policies and interventions.
• Scale refers to the application of dynamic models at different scales. Moreover, the SDM considers a system as a whole, analyzing and focusing on its components and sub-components.
In fact, SDMs are mostly applied to municipal or metropolitan scales. LV models are generally employed to provincial and sub-regional scales and to those territories with a rural vocation. specific software, such as STELLA, Venism and Powerism, that formulate themselves the ODEs from which the scenarios' simulations are produced. On the other hand, LV models are generally employed through mathematical software, such as MatLab and Mathematica Software, and these need to write manually the ODEs to obtain the prediction of scenarios ( Figure 6). In this sense, both the dynamic models use the ODEs as an output, but in different ways. From the point of view of the availability, both dynamic models may be written through specific packages in open programming languages, such "deSolve" for R, "Simupy" for Python, "Mat Cont for Matlab" and "Nova modeler" for ecological modelling.

•
Integration refers to the capability of DMs to integrate different techniques and evaluation methodologies. For instance, the considered dynamic models are a suitable tool to being integrated with Multicriteria Analysis (MCA) [75], as well as with the Agent-Based Models (ABM) [94] and Hedonic Price Model (HPM) [95]. Specifically, MCA can be used at two different phases: (1) at the beginning, to support the problem articulation and the identification of the variables to be included in the model; (2) after the scenarios' simulation to support the evaluation of the different performances through final score calculation or ranking elaboration. Shafiei et al. [96] integrate SDM and Agent-Based Models to better understand the effects, not only on the system but also on the agent of the transition to sustainable mobility.

•
Mapping is intended as the possibility to visualize the scenarios using GIS-based methods and the possibility to interact the dynamic model and the GIS interface through a programming language (e.g., QGIS and Python). Actually, the integration of DMs simulation results into GIS is developed by users in specific plug-ins (e.g., PANDORA 3.0 [97]) or by using specific coding platforms (e.g., QGIS Python console) and to get a spatial visualization of the output. Despite the requirement of specific competences to manage DMs in GIS environment, the users may support decision makers in better interpreting certain dynamics related to urban resilience by visualizing spatially the output of the dynamic model in a final map and therefore, identifying specific policies and solutions.

•
Scenario planning refers to the prediction of future scenarios and the definition for each scenario of objectives and strategies. Both SDM and LV models allow to predict the way variables evolve, starting from the state of art conditions (t0) [50]. In this sense, both the SDM and the LV models are useful supports for the decision makers for identifying the most critical areas and adopting specific policies and interventions.
• Scale refers to the application of dynamic models at different scales. Moreover, the SDM considers a system as a whole, analyzing and focusing on its components and sub-components. In fact, SDMs are mostly applied to municipal or metropolitan scales. LV models are generally employed to provincial and sub-regional scales and to those territories with a rural vocation. specific software, such as STELLA, Venism and Powerism, that formulate themselves the ODEs from which the scenarios' simulations are produced. On the other hand, LV models are generally employed through mathematical software, such as MatLab and Mathematica Software, and these need to write manually the ODEs to obtain the prediction of scenarios ( Figure 6). In this sense, both the dynamic models use the ODEs as an output, but in different ways. From the point of view of the availability, both dynamic models may be written through specific packages in open programming languages, such "deSolve" for R, "Simupy" for Python, "Mat Cont for Matlab" and "Nova modeler" for ecological modelling.

•
Integration refers to the capability of DMs to integrate different techniques and evaluation methodologies. For instance, the considered dynamic models are a suitable tool to being integrated with Multicriteria Analysis (MCA) [75], as well as with the Agent-Based Models (ABM) [94] and Hedonic Price Model (HPM) [95]. Specifically, MCA can be used at two different phases: (1) at the beginning, to support the problem articulation and the identification of the variables to be included in the model; (2) after the scenarios' simulation to support the evaluation of the different performances through final score calculation or ranking elaboration. Shafiei et al. [96] integrate SDM and Agent-Based Models to better understand the effects, not only on the system but also on the agent of the transition to sustainable mobility.

•
Mapping is intended as the possibility to visualize the scenarios using GIS-based methods and the possibility to interact the dynamic model and the GIS interface through a programming language (e.g., QGIS and Python). Actually, the integration of DMs simulation results into GIS is developed by users in specific plug-ins (e.g., PANDORA 3.0 [97]) or by using specific coding platforms (e.g., QGIS Python console) and to get a spatial visualization of the output. Despite the requirement of specific competences to manage DMs in GIS environment, the users may support decision makers in better interpreting certain dynamics related to urban resilience by visualizing spatially the output of the dynamic model in a final map and therefore, identifying specific policies and solutions.

•
Scenario planning refers to the prediction of future scenarios and the definition for each scenario of objectives and strategies. Both SDM and LV models allow to predict the way variables evolve, starting from the state of art conditions (t0) [50]. In this sense, both the SDM and the LV models are useful supports for the decision makers for identifying the most critical areas and adopting specific policies and interventions.
• Scale refers to the application of dynamic models at different scales. Moreover, the SDM considers a system as a whole, analyzing and focusing on its components and sub-components. In fact, SDMs are mostly applied to municipal or metropolitan scales. LV models are generally employed to provincial and sub-regional scales and to those territories with a rural vocation. specific software, such as STELLA, Venism and Powerism, that formulate themselves the ODEs from which the scenarios' simulations are produced. On the other hand, LV models are generally employed through mathematical software, such as MatLab and Mathematica Software, and these need to write manually the ODEs to obtain the prediction of scenarios ( Figure 6). In this sense, both the dynamic models use the ODEs as an output, but in different ways. From the point of view of the availability, both dynamic models may be written through specific packages in open programming languages, such "deSolve" for R, "Simupy" for Python, "Mat Cont for Matlab" and "Nova modeler" for ecological modelling.

•
Integration refers to the capability of DMs to integrate different techniques and evaluation methodologies. For instance, the considered dynamic models are a suitable tool to being integrated with Multicriteria Analysis (MCA) [75], as well as with the Agent-Based Models (ABM) [94] and Hedonic Price Model (HPM) [95]. Specifically, MCA can be used at two different phases: (1) at the beginning, to support the problem articulation and the identification of the variables to be included in the model; (2) after the scenarios' simulation to support the evaluation of the different performances through final score calculation or ranking elaboration. Shafiei et al. [96] integrate SDM and Agent-Based Models to better understand the effects, not only on the system but also on the agent of the transition to sustainable mobility.

•
Mapping is intended as the possibility to visualize the scenarios using GIS-based methods and the possibility to interact the dynamic model and the GIS interface through a programming language (e.g., QGIS and Python). Actually, the integration of DMs simulation results into GIS is developed by users in specific plug-ins (e.g., PANDORA 3.0 [97]) or by using specific coding platforms (e.g., QGIS Python console) and to get a spatial visualization of the output. Despite the requirement of specific competences to manage DMs in GIS environment, the users may support decision makers in better interpreting certain dynamics related to urban resilience by visualizing spatially the output of the dynamic model in a final map and therefore, identifying specific policies and solutions.

•
Scenario planning refers to the prediction of future scenarios and the definition for each scenario of objectives and strategies. Both SDM and LV models allow to predict the way variables evolve, starting from the state of art conditions (t0) [50]. In this sense, both the SDM and the LV models are useful supports for the decision makers for identifying the most critical areas and adopting specific policies and interventions.
• Scale refers to the application of dynamic models at different scales. Moreover, the SDM considers a system as a whole, analyzing and focusing on its components and sub-components. In fact, SDMs are mostly applied to municipal or metropolitan scales. LV models are generally employed to provincial and sub-regional scales and to those territories with a rural vocation. Table 6. Lotka-Volterra models and System Dynamic Models: summarizing comparison matrix (Authors' elaboration, 2019).

Nature
Essence and characters *

Input
Use of qualitative and quantitative data Participatory process Use of different spatial scales

Scenario simulation
Time scale * Lotka-Volterra model is used to show the functioning of the system, whereas the System Dynamic Model is a tool used to study and analyze the model or the system.
In particular, a number of criteria have been considered for this analysis. The criteria are selected according to relevant literature review [48,54,55] and to authors' researches: • Nature highlights the different essence and characteristics of both dynamic models. On one hand, the Lotka-Volterra are models that aim to explore the dynamic functions of a given environmental system N, whereas the SDM models may be considered as a tool used to study and analyze the model or the system.

•
Input is intended as the modalities to insert and deal with data at different spatial scales, as well as the possibility to integrate the participatory process. Generally, the considered dynamic models allow the insert of only quantitative data and the employment of different spatial scales (from local to regional and superior). As far as the participatory process is concerned in the SDM models, the decision makers may be integrated since the early phases of the process by using causal loops ( Figure 1) that facilitate the interpretation of the system functioning and the integration of different stakeholders' perspectives [14,50]. In the LV models, the participatory process may be integrated only by other evaluation procedures, such as the Multicriteria Analysis (MCA), by using a system of indicators and indices [79,87].

•
Output refers to the final result produced through the considered dynamic models, such as the scenario simulation, the use of the time scale, the spatial scale, the graphical representation and the sensitivity analysis with the aim to validate the scenarios produced. Particularly, both SDM and LV models simulate possible future scenarios and these represent, generally, the final output through a graphic plot in that the linear function is represented. Unlike the LV models, the SDM models show, since the initial phase, a graphical representation of the relations between the considered variables and they allow to make, after the scenario simulation, a sensitivity analysis. These two DMs use, in different ways the time scale: the SDM model use a real time scale that may be traduced in months, years or centuries, whereas the LV model uses an arbitrary time scale that may be subdivided in an initial phase when the function starts with the state of art conditions (t 0 ), transitory phase, when the linear function evolves in terms of growth or degrowth, and a final phase, when the linear function became stable. The arbitrary time scale may be traduced in a real time scale by considering the historical series of the analyzed parameters [74]. Sensitivity analysis is a valuable procedure for testing the model response with respect to the variation of parameter values, as well as to identify those parameters that have more impact than the others on the investigated phenomenon [88]. Sensitivity analysis can increase the reliability of the model and thus, reduce the uncertainty of parameters used in the models. A very common sensitivity test is the One-At-Time approach (OAT) [89] that is often used in Multicriteria Analysis as final tuning [75,90,91]. This, in fact, facilitates the scenarios' assessment when actors and stakeholders are involved in a participatory decision-making process [92,93]. • Software refers to the availability of software and the modalities to solve the Ordinary Differential Equations (ODEs). On one hand, the SDM models are characterized by the use of specific software, such as STELLA, Venism and Powerism, that formulate themselves the ODEs from which the scenarios' simulations are produced. On the other hand, LV models are generally employed through mathematical software, such as MatLab and Mathematica Software, and these need to write manually the ODEs to obtain the prediction of scenarios ( Figure 6). In this sense, both the dynamic models use the ODEs as an output, but in different ways. From the point of view of the availability, both dynamic models may be written through specific packages in open programming languages, such "deSolve" for R, "Simupy" for Python, "Mat Cont for Matlab" and "Nova modeler" for ecological modelling.

•
Integration refers to the capability of DMs to integrate different techniques and evaluation methodologies. For instance, the considered dynamic models are a suitable tool to being integrated with Multicriteria Analysis (MCA) [75], as well as with the Agent-Based Models (ABM) [94] and Hedonic Price Model (HPM) [95]. Specifically, MCA can be used at two different phases: (1) at the beginning, to support the problem articulation and the identification of the variables to be included in the model; (2) after the scenarios' simulation to support the evaluation of the different performances through final score calculation or ranking elaboration. Shafiei et al. [96] integrate SDM and Agent-Based Models to better understand the effects, not only on the system but also on the agent of the transition to sustainable mobility.

•
Mapping is intended as the possibility to visualize the scenarios using GIS-based methods and the possibility to interact the dynamic model and the GIS interface through a programming language (e.g., QGIS and Python). Actually, the integration of DMs simulation results into GIS is developed by users in specific plug-ins (e.g., PANDORA 3.0 [97]) or by using specific coding platforms (e.g., QGIS Python console) and to get a spatial visualization of the output. Despite the requirement of specific competences to manage DMs in GIS environment, the users may support decision makers in better interpreting certain dynamics related to urban resilience by visualizing spatially the output of the dynamic model in a final map and therefore, identifying specific policies and solutions.

•
Scenario planning refers to the prediction of future scenarios and the definition for each scenario of objectives and strategies. Both SDM and LV models allow to predict the way variables evolve, starting from the state of art conditions (t 0 ) [50]. In this sense, both the SDM and the LV models are useful supports for the decision makers for identifying the most critical areas and adopting specific policies and interventions. • Scale refers to the application of dynamic models at different scales. Moreover, the SDM considers a system as a whole, analyzing and focusing on its components and sub-components. In fact, SDMs are mostly applied to municipal or metropolitan scales. LV models are generally employed to provincial and sub-regional scales and to those territories with a rural vocation.

Conclusions and Future Perspectives
This paper explored the role of the family of dynamic models (DMs) and their characteristics as support in the decision-making process for evaluating complex phenomena, as in the case of the resilience of urban and territorial systems. Particularly, the study on the state of the art of resilience, urban resilience, dynamic models and urban simulation methods provided an epistemological contribution to the issue. The examples considered in this paper can be useful to further explore the opportunities of analysis application to investigate the key variables of issues in cities and territories. The comparison matrix highlighted commonalities, differences and potential synergies between the SDM and LV models. Both the SDM and LV models may be considered reliable supporting tools for policy planning, thanks to their ability to predict possible future behaviors of selected key variables, thus helping actors and stakeholders to identify and prioritize shared objectives and strategies for increasing urban resilience. In fact, these DMs are able to integrate the scientific knowledge available in literature within the evaluation procedure with specific expert knowledge elicited in the participatory modelling processes [98]. Some final remarks with respect to building more resilient systems [99] could be:

•
These DMs are currently considered as some of the most promising models for understanding multi-dimensional problems related to urban and territorial systems.

•
If experiments are impossible in the real world, simulations become the main way we can learn effectively about the dynamics of complex systems. Dynamic models are the most appropriate techniques to simulate complex and dynamic systems with the aim of developing policy and learning to effectively manage the system [50,100]. • These models are able to predict the effects of the actions over time on the state of the system. For this reason, both the DMs considered can be applied to evaluate the possible effects of urban and territorial policies in order to enhance urban resilience.

•
The integration of dynamic models with urban simulation methods makes it possible to support data collection and elaboration, problem structuring, and facilitate the involvement of actors and stakeholders [12,88,[101][102][103].
early stages of the process. Finally, an integrated tool will be developed to evaluate possible effects of natural or anthropic disasters that could compromise the resilience performance of systems, also evaluating the economic losses caused by the perturbations of the system.

Conflicts of Interest:
The authors declare no conflict of interest.