Periodic solutions of discrete time periodic time-varying coupled systems on networks

Highlights: • We construct a model of discrete time periodic time-varying coupled systems on networks. • We present sufficient criteria for existence of periodic solutions. • A systematic method combining coincidence degree theory, Lyapunov method, and graph theory is provided and applied to discrete time Cohen–Grossberg Neural Networks. • The existence criteria are shown in terms of the topology property of the network. - Abstract: In this paper, we consider the existence of periodic solutions for discrete time periodic time-varying coupled systems on networks (DPTCSN). Some novel sufficient conditions are obtained to guarantee the existence of periodic solutions for DPTCSN, which have a close relation to the topology property of the corresponding network. Our approach is based on the continuation theorem of coincidence degree theory, generalized Kirchhoff's matrix tree theorem in graph theory, Lyapunov method and some new analysis techniques. The approach is applied to the existence of periodic solutions for discrete time Cohen–Grossberg Neural Networks (CGNN). Finally, an example and numerical simulations are provided to illustrate the effectiveness of our theoretical results.