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

Probability;Analysis of PDEs