Exponential stability of the stationary distribution of a mean field of spiking neural network - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue Journal of Differential Equations Année : 2018

Exponential stability of the stationary distribution of a mean field of spiking neural network

Audric Drogoul
  • Fonction : Auteur
  • PersonId : 980735
Romain Veltz

Résumé

In this work, we study the exponential stability of the stationary distribution of a McKean-Vlasov equation, of nonlinear hyperbolic type which was recently derived in \cite{de_masi_hydrodynamic_2015,fournier_toy_2016}. We complement the convergence result proved in \cite{fournier_toy_2016} using tools from dynamical systems theory. Our proof relies on two principal arguments in addition to a Picard-like iteration method. First, the linearized semigroup is positive which allows to precisely pinpoint the spectrum of the infinitesimal generator. Second, we use a time rescaling argument to transform the original quasilinear equation into another one for which the nonlinear flow is differentiable. Interestingly, this convergence result can be interpreted as the existence of a locally exponentially attracting center manifold for a hyperbolic equation.
Fichier principal
Vignette du fichier
rapport-hal.pdf (865.1 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01290264 , version 1 (08-04-2016)
hal-01290264 , version 2 (13-04-2018)

Identifiants

Citer

Audric Drogoul, Romain Veltz. Exponential stability of the stationary distribution of a mean field of spiking neural network. Journal of Differential Equations, 2018, ⟨10.1016/j.jde.2020.08.001⟩. ⟨hal-01290264v2⟩
566 Consultations
414 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More