Non-homogeneous Wilson-Cowan model

Abstract

A Wilson-Cowan model with periodic input to both the excitatory and inhibitory cells is analyzed. The analysis of the non-homogeneous nonlinear system is made possible by reducing it to a single periodic differential equation of first order, which is shown to have the same number and type of periodic solutions as the system of equations. In the relevant parameter region, the behavior of the system can be determined by examining the slope field of the first-order equation. Numerical examples are given of several systems, one of which is bistable and another in which input-produced bursting occurs.