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In this paper we prove the propagation of chaos property for an ensemble ofinteracting neurons subject to independent Brownian noise. The propagation ofchaos property means that in the large network size limit, the neurons behaveas if they are probabilistically independent. The model for the internaldynamics of the neurons is taken to be that of Wilson and Cowan, and weconsider there to be multiple different populations. The synaptic connectionsare modelled with a nonlinear `electrical' model. The nonlinearity of thesynaptic connections means that our model lies outside the scope of classicalpropagation of chaos results. We obtain the propagation of chaos result bytaking advantage of the fact that the mean-field equations are Gaussian, whichallows us to use Borell's Inequality to prove that its tails decayexponentially.

Mean Field Dynamics of a Network of Wilson-Cowan Neurons with Electrical Synapses