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April 2021 Periodicity induced by noise and interaction in the kinetic mean-field FitzHugh–Nagumo model
Eric Luçon, Christophe Poquet
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Ann. Appl. Probab. 31(2): 561-593 (April 2021). DOI: 10.1214/20-AAP1598


We consider the long-time behavior of a population of mean-field oscillators modeling the activity of interacting excitable neurons in a large population. Each neuron is represented by its voltage and recovery variables, which are the 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.


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Eric Luçon. Christophe Poquet. "Periodicity induced by noise and interaction in the kinetic mean-field FitzHugh–Nagumo model." Ann. Appl. Probab. 31 (2) 561 - 593, April 2021.


Received: 1 June 2019; Revised: 1 May 2020; Published: April 2021
First available in Project Euclid: 1 April 2021

Digital Object Identifier: 10.1214/20-AAP1598

Primary: 60K35
Secondary: 35K55 , 35Q84 , 37N25 , 82C26 , 82C31 , 92B20

Keywords: excitable systems , FitzHugh–Nagumo model , McKean–Vlasov process , mean-field systems , noise-induced dynamics , nonlinear Fokker–Planck equation , slow-fast dynamics , Wasserstein distance

Rights: Copyright © 2021 Institute of Mathematical Statistics


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Vol.31 • No. 2 • April 2021
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