  In this work, we propose a nonlinear stochastic model of a network of
stochastic spiking neurons. We heuristically derive the mean-field limit of
this system. We then design a Monte Carlo method for the simulation of the
microscopic system, and a finite volume method (based on an upwind implicit
scheme) for the mean-field model. The finite volume method respects numerical
versions of the two main properties of the mean-field model, conservation and
positivity, leading to existence and uniqueness of a numerical solution. As the
size of the network tends to infinity, we numerically observe propagation of
chaos and convergence from an individual description to a mean-field
description. Numerical evidences for the existence of a Hopf bifurcation
(synonym of synchronised activity) for a sufficiently high value of
connectivity, are provided.
