  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 provide a proof of a conjecture originally
proposed by J. Touboul and P. Robert regarding the bistable nature of a
specific instance of this neuronal model.
