A note on a neuron network model with diffusion

Abstract

We study the dynamics of inhomogeneous neuronal networks parametrized by a real number σ and structured by the time elapsed since the last discharge. The dynamics are governed by the parabolic PDE which describes the probability density of neurons with elapsed time s after its last discharge. We prove existence and uniqueness of a solution to the model. Moreover, we show that under some conditions on the connectivity and the firing rate, the networks exhibit total desynchronization.