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
Article Dans Une Revue Mathematical Neuroscience and Applications Année : 2024

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

Résumé

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

Dates et 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. Mathematical Neuroscience and Applications, 2024, ⟨10.46298/mna.12583⟩. ⟨hal-02488915⟩
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