On the effect of a Gaussian firing rate function on the dynamics of a network of Wilson-Cowan populations

We study the effect of a Gaussian firing rate function on the dynamics of a neural network of coupled Wilson-Cowan equations. Bifurcation analysis shows that an extra stable high activity equilibrium exists in addition to the normal behavior. Two populations are coupled by their excitatory subpopulations and a bifurcation analysis shows periodic solutions, some of which are not found using the original equations. Simulations with a large network of coupled populations show activity spread from a stable high activity population which drives the network. Using a propagation delay between populations, we analyze the stability of the various periodic solutions. It is shown that the coupling strength and propagation delay have a large influence on the stability of these periodic solutions. We classify patterns and link their appearance with the coupling strength and time delay in a large network of populations.