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Article Dans Une Revue The Annals of Applied Probability Année : 2021

Periodicity induced by noise and interaction in the kinetic mean-field FitzHugh-Nagumo model

Résumé

We consider the long-time behavior of a population of mean-field oscillators modeling the activity of interacting excitable neurons in large population. Each neuron is represented by its voltage and recovery variables, which are solution to a FitzHugh-Nagumo system, and interacts with the rest of the population through a mean-field linear coupling, in the presence of noise. The aim of the paper is to study the emergence of collective oscillatory behaviors induced by noise and interaction on such a system. The main difficulty of the present analysis is that we consider the kinetic case, where interaction and noise are only imposed on the voltage variable. We prove the existence of a stable cycle for the infinite population system, in a regime where the local dynamics is small.

Dates et versions

hal-01911080 , version 1 (02-11-2018)

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Eric Luçon, Christophe Poquet. Periodicity induced by noise and interaction in the kinetic mean-field FitzHugh-Nagumo model. The Annals of Applied Probability, 2021, 31 (2), pp.561-593. ⟨10.1214/20-AAP1598⟩. ⟨hal-01911080⟩
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