Switches of oscillations in coupled networks with multiple time delays

This paper reveals the behaviors of a coupled network consisting of four sub-networks each with two neurons and multiple couplings between the sub-networks. Time delays are introduced into the internal connections within the sub-networks and the couplings between the sub-networks. The stability switches of the network equilibrium are analyzed and the conditions for the existence of periodic oscillations are given by discussing the associated characteristic equation. Numerical simulations are performed to illustrate the effectiveness of the obtained results and interesting network behaviors are observed, such as multiple switches of periodic oscillations.