PERIODICITY INDUCED BY NOISE AND INTERACTION IN THE KINETIC MEAN-FIELD FITZHUGH-NAGUMO MODEL

• 成果类型: Article
• 署名作者: Lucon, Eric; Poquet, Christophe
• 署名单位: Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/20-AAP1598
• 发表日期: 2021
• 页码: 561-593
• 关键词: long-time dynamics; invariant-manifolds; Synchronization; BEHAVIOR

摘要

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.