  In this article, we are interested in the behavior of a fully connected
network of $N$ neurons, where $N$ tends to infinity. We assume that the neurons
follow the stochastic FitzHugh-Nagumo model, whose specificity is the
non-linearity with a cubic term. We prove a result of uniform in time
propagation of chaos of this model in a mean-field framework. We also exhibit
explicit bounds. We use a coupling method initially suggested by A. Eberle
(arXiv:1305.1233), and recently extended in (1805.11387), known as the
reflection coupling. We simultaneously construct a solution of the $N$-particle
system and $N$ independent copies of the non-linear McKean-Vlasov limit in such
a way that, considering an appropriate semi-metric that takes into account the
various possible behaviors of the processes, the two solutions tend to get
closer together as $N$ increases, uniformly in time. The reflection coupling
allows us to deal with the non-convexity of the underlying potential in the
dynamics of the quantities defining our network, and show independence at the
limit for the system in mean field interaction with sufficiently small
Lipschitz continuous interactions.
