Abstract
The biological process of individuals moving from an active state to a passive one when environmental conditions become adverse is formalized. From the mathematical point of view, this results in a universal linear superstructure to nonlinear models of ecosystems. It is found that under a certain choice of transition rates, the oscillatory instability can be stabilized and population survivability can be increased. Processes of competition, predation, and cyclic coadaptation of populations in a variable environment are studied.
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References
B. P. Ushakov, “Evolutionary Value of Temperature Adaptation of Animals,” Usp. Sovrem. Biol. 93(2), 302–309 (1982).
R. S. Ushatinskaya, Hidden Life and Anabiosis (Nauka, Moscow, 1990) [in Russian].
R. P. Getsina and V. G. Il’ichev, “Passive Form of Existence is a Stabilizing Factor in the Dynamics of Interacting Populations,” Izv. Severo-Kav. Nauch. Tsentra Vysshei Shkoly Estestvennykh Nauk, No. 3, 131–136 (1986).
G. E. Hatchinson, “Circular Causal System in Ecology, Ann. N. Y. Acad. Sci, 50, 221–246 (1948).
V. G. Il’ichev, “Mechanism of Generation of Passive States and Stabilization of Dynamic Systems,” Kibern. Sistemn. Anal., No. 3, 128–137 (1995).
V. G. Il’ichev, “On Technology of Constructing Simulation Models of Ecological Systems. Adaptation Mechanisms,” Mat. Model. 4(3), 11–19 (1992).
V. G. Il’ichev and O. A. Il’icheva, “Analysis of Competition Models in Constant and Periodic Environments,” Mat. Model. 14(3), 71–83 (2002).
V. G. Il’ichev, O. A. Il’icheva, and V. Yu. Voronin, “Selection Criteria in Systems “All against All” and “All against One,” Obozrenie Prikl. i Promysh. Matematiki 6(2), 311–317 (1999).
V. G. Il’ichev, “Delta-Function and Investigation of Volterra Ecological Models in a Variable Environment,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 4, 23–33 (1998).
P. Troyan, Factorial Ecology (Vishcha Shkola, Kiev, 1989) [in Russian].
D. E. Contois, “Kinetics of Bacterial Growth Relationship between Population Density and Specific Growth Rate of Continuous Culture,” J. Gen. Microbiol., Nos. 1–2, 40 (1959).
V. G. Il’ichev, “Adaptation of Parameters in Population Models,” Zhurnal Obshch. Biologii 66(2), 171–179 (2005).
P. S. Giller, Community, Structure and the Niche. Outline Studies in Ecology (Chapman and Hall, London and New York, 1984; Mir, Moscow, 1988).
V. G. Il’ichev, “Global Properties of Nonautonomous Dynamical Systems and Their Application to Models of Competition,” Izv. Ross. Akad. Nauk, Teor. Sist. Upr., No. 5, 1–8 (2002) [Comp. Syst. Sci. 41 (5), 677–684 (2003)].
V. I. Opoitsev, Nonlinear Systems Static (Nauka, Moscow, 1986) [in Russian].
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Original Russian Text © V.G. Il’ichev, 2008, published in Izvestiya Akademii Nauk. Teoriya i Sistemy Upravleniya, 2008, No. 5, pp. 166–176.
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Il’ichev, V.G. Active and passive states in ecological models (stabilization, adaptation, and survivability). J. Comput. Syst. Sci. Int. 47, 830–839 (2008). https://doi.org/10.1134/S1064230708050171
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DOI: https://doi.org/10.1134/S1064230708050171