On synchronization of networks of Wilson–Cowan oscillators with diffusive coupling. (September 2016) - Ahmadizadeh, Saeed; Nešić, Dragan; Freestone, Dean R.; Grayden, David B.
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 averaging and the Chetaev theorem, while, for the remaining part, we use a recently proposed numerical approach. Sufficient conditions are established to highlight the effect of network topology on synchronous behavior when the interconnection is undirected. These conditions are utilized to address points that have been previously reported in the literature through simulations: synchronization might persist or vanish in the presence of perturbation in the interconnection gains. Simulation results confirm and illustrate our results.