On synchronization of networks of Wilson-Cowan oscillators with diffusive coupling

Abstract

We investigate the problem of synchronization in a network of homogeneous Wilson-Cowan oscillators with diffusive coupling. Such networks can be used to model the behavior of populations of neurons in cortical tissue, referred to as neural mass models. A new approach is proposed to address conditions for local synchronization for this type of neural mass models. By analyzing the linearized model around a limit cycle, we study synchronization within a network with direct coupling. We use both analytical and numerical approaches to link the presence or absence of synchronized behavior to the location of eigenvalues of the Laplacian matrix. For the analytical part, we apply two-time scale avera..