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Modeling Fireflies Synchronization

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A Mathematical Modeling Approach from Nonlinear Dynamics to Complex Systems

Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 22))

Abstract

Albeit synchronous behavior of some fireflies species is one of the paradigmatic examples of synchronization, there are not many efforts to model in a realistic way this astounding phenomenon. One of the most important features of fireflies synchronization is the cooperative behavior of many fireflies giving rise to the emergency of synchronization without any leader, a fact that took a long time to be recognized. In this chapter, we review the main attempts to build models allowing the explanation of how and why fireflies synchronize. The starting point is qualitative models based on simple observations. The latter served to formulate original mathematical models enabling not only to explain fireflies synchronization but also some other collective phenomena. Integrate-and-fire oscillators (IFOs) constitute an emblematic model to describe the fireflies’ synchronous behavior, and they have also inspired ones to build electronic circuits with similar features and adapted to fireflies in the sense that they communicate with each other by means of light-pulses. The above-mentioned electronic circuits received the name of electronic fireflies or more technically, light-controlled oscillators (LCOs). These engines allowed a systematic study of synchronization from experimental, theoretical, and numerical viewpoints. They have also been used in a wide variety of situations ranging from simple cases of identical oscillators to scenarios where populations of dissimilar oscillators whose interaction does explain synchronization as well as the response to synchronization, a widespread phenomenon occurring in fireflies. The obtained results and the well-knowledge of the models allow introducing simplified versions. These simplifying ideas might be taken as toy models in the strict sense of the word because based on these models it is possible to construct a game. This minimalist model is called the “solitary flash” game (SFG), a game where fireflies are the players and they can synchronize, thanks to simple rules. Finally, we discuss briefly the potentials of the fireflies synchronization paying particular attention to its application in communication networks.

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Acknowledgements

J.K. acknowledges IRTG 1740 (DFG). J.-L.D. is senior research associate from the Belgian National Fund for Scientific Research (FNRS).

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Authors and Affiliations

  1. Instituto de Investigaciones Físicas, Universidad Mayor de San Andrés, La Paz, Bolivia

    Gonzalo Marcelo Ramírez-Ávila & Stéphanie Depickère

  2. Institut für Physik, Humboldt-Universität zu Berlin, Berlin, Germany

    Jürgen Kurths

  3. Potsdam Institut für Klimafolgenforschung, Potsdam, Germany

    Jürgen Kurths

  4. Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen, UK

    Jürgen Kurths

  5. Department of Control Theory, Nizhny Novgorod State University, Nizhny Novgorod, Russia

    Jürgen Kurths

  6. Center for Nonlinear Phenomena and Complex Systems, Brussels, Belgium

    Jean-Louis Deneubourg

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  1. Gonzalo Marcelo Ramírez-Ávila
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  2. Jürgen Kurths
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  3. Stéphanie Depickère
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  4. Jean-Louis Deneubourg
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Correspondence to Gonzalo Marcelo Ramírez-Ávila .

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  1. Instituto Nacional de Pesquisas Espaciais – INPE, São José dos Campos, Brazil

    Elbert E. N. Macau

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Ramírez-Ávila, G.M., Kurths, J., Depickère, S., Deneubourg, JL. (2019). Modeling Fireflies Synchronization. In: Macau, E. (eds) A Mathematical Modeling Approach from Nonlinear Dynamics to Complex Systems . Nonlinear Systems and Complexity, vol 22. Springer, Cham. https://doi.org/10.1007/978-3-319-78512-7_8

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