Hypothèse de synchronisation dans le modèle de Winfree

OUKIL, W; KESSI, A; THIEULLEN, Ph

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OUKIL, W
Institut de Mathématiques de Bordeaux [IMB]
Université Yahia Fares de Médéa

KESSI, A
Université des Sciences et de la Technologie Houari Boumediene = University of Sciences and Technology Houari Boumediene [Alger] [USTHB]

THIEULLEN, Ph
Institut de Mathématiques de Bordeaux [IMB]

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Document de travail - Pré-publication

Résumé en anglais

We consider $N$ oscillators coupled by a mean field as in the Winfree model. The model is governed by two parameters: the coupling strength $\kappa$ and the spectrum width $\gamma$ of the frequencies of each oscillator. In the uncoupled regime, $\kappa=0$, each oscillator possesses its own natural frequency, and the difference between the phases of any two oscillators grows linearly in time. We say that $N$ oscillators are synchronized if the difference between any two phases is uniformly bounded in time. We identify a new hypothesis for the existence of synchronization. The domain in $(\gamma,\kappa)$ of synchronization contains coupling values that are both weak and strong. Moreover the domain is independent of the number of oscillators and the distribution of the frequencies. We give a numerical counter-example which shows that this hypothesis is necessary for the existence of synchronization.< Réduire

Mots clés en anglais

desynchronization

synchronization

Winfree Model

Coupled oscillators

periodic orbit

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