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

mna:12583 - Mathematical Neuroscience and Applications, September 27, 2024, Volume 4 - https://doi.org/10.46298/mna.12583
A mean-field model of Integrate-and-Fire neurons: non-linear stability of the stationary solutionsArticle

Authors: Quentin Cormier ORCID1

  • 1 Inria, CMAP, CNRS, École polytechnique, Institut Polytechnique de Paris

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.


Volume: Volume 4
Published on: September 27, 2024
Accepted on: June 25, 2024
Submitted on: November 22, 2023
Keywords: Mathematics - Probability,Mathematics - Analysis of PDEs,60H10 (Primary) 60K35, 45D05, 37A30 (Secondary)

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