Time evolution of a mean-field generalized contact process

Abstract

We investigate the macroscopic time evolution and stationary states of a mean field discrete voltage neuron model, or equivalently, a generalized contact process in . The model is described by a coupled set of nonlinear integral-differential equations. It was inspired by a model of neurons with discrete voltages evolving by a stochastic integrate and fire mechanism. We obtain a complete solution in the spatially uniform case and partial solutions in the general case. The system has one or more fixed points and also traveling wave solutions.