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The European Physical Journal Special Topics

, Volume 227, Issue 10–11, pp 1267–1279 | Cite as

Revisiting asymptotic periodicity in networks of degrade-and-fire oscillators

  • Bastien FernandezEmail author
Regular Article
Part of the following topical collections:
  1. Advances in Nonlinear Dynamics of Complex Networks: Adaptivity, Stochasticity, Delays

Abstract

Networks of degrade-and-fire oscillators are elementary models of populations of synthetic gene circuits with negative feedback, which show elaborate phenomenology while being amenable to mathematical analysis. In addition to thorough investigation in various examples of interaction graphs, previous studies have obtained conditions on interaction topology and strength that ensure that asymptotic behaviors are periodic (assuming that the so-called firing sequence is itself periodic and involves all nodes). Here, we revisit and extend these conditions and we analyse the dynamics in a case of unidirectional periodic chain. This example shows in particular that the updated conditions for asymptotic periodicity are optimal. Altogether, our results provide a novel instance of direct impact of the topology of interactions in the global dynamics of a collective system. Dedicated to the memory of Valentin Afraimovich.

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Copyright information

© EDP Sciences, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Laboratoire de Probabilités, Statistique et Modélisation CNRS – Univ. Paris 7 Denis Diderot – Sorbonne Univ.Paris Cedex 13France

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