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Modeling Fireflies Synchronization

  • Gonzalo Marcelo Ramírez-Ávila
  • Jürgen Kurths
  • Stéphanie Depickère
  • Jean-Louis Deneubourg
Chapter
Part of the Nonlinear Systems and Complexity book series (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.

Notes

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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Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Gonzalo Marcelo Ramírez-Ávila
    • 1
  • Jürgen Kurths
    • 2
    • 3
    • 4
    • 5
  • Stéphanie Depickère
    • 1
  • Jean-Louis Deneubourg
    • 6
  1. 1.Instituto de Investigaciones FísicasUniversidad Mayor de San AndrésLa PazBolivia
  2. 2.Institut für PhysikHumboldt-Universität zu BerlinBerlinGermany
  3. 3.Potsdam Institut für KlimafolgenforschungPotsdamGermany
  4. 4.Institute for Complex Systems and Mathematical BiologyUniversity of AberdeenAberdeenUK
  5. 5.Department of Control TheoryNizhny Novgorod State UniversityNizhny NovgorodRussia
  6. 6.Center for Nonlinear Phenomena and Complex SystemsBrusselsBelgium

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