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arXiv · 2002.08649

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

Quentin Cormier
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Abstract

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.

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Quentin Cormier. 2020-02-20. A mean-field model of Integrate-and-Fire neurons: non-linear stability of the stationary solutions. https://doi.org/10.46298/mna.12583

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