A mean-field model of Integrate-and-Fire neurons: non-linear stability of the stationary solutions - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Preprints, Working Papers, ... Year : 2023

A mean-field model of Integrate-and-Fire neurons: non-linear stability of the stationary solutions

Abstract

We investigate a stochastic network composed of Integrate-and-Fire spiking neurons, focusing on its mean-field asymptotic behavior. We consider an invariant probability measure of the McKean-Vlasov equation and establish an explicit sufficient condition for ensuring the local stability of this invariant distribution. Furthermore, we provide a proof of a conjecture originally proposed by P. Robert and J. Touboul regarding the bistable nature of a specific instance of this neuronal model.

Dates and versions

hal-02488915 , version 1 (24-02-2020)

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Quentin Cormier. A mean-field model of Integrate-and-Fire neurons: non-linear stability of the stationary solutions. 2023. ⟨hal-02488915⟩
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