Time evolution of a mean-field generalized contact process

Abstract

We investigate the macroscopic time evolution and stationary states of a mean field generalized contact process in ${\mathbb{R}}^d$. 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.

20 pages, 2 figures

References in corpus (1)

• Stochastic Wilson-Cowan models of neuronal network dynamics with memory and delay

Cited by in corpus (1)

• Metastability in a Stochastic System of Spiking Neurons with Leakage