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We investigate a stochastic network composed of Integrate-and-Fire spikingneurons, focusing on its mean-field asymptotic behavior. We consider aninvariant probability measure of the McKean-Vlasov equation and establish anexplicit sufficient condition for ensuring the local stability of thisinvariant distribution. Furthermore, we provide a proof of a conjectureoriginally proposed by P. Robert and J. Touboul regarding the bistable natureof a specific instance of this neuronal model.

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