A note on a neuron network model with diffusion
Philippe Michel, Suman Kumar Tumuluri · Discrete and Continuous Dynamical Systems - B · 2020
We study the dynamics of an inhomogeneous neuronal network parametrized by a real number $ \sigma $ 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 network exhibits total desynchronization.