The existence, uniqueness and global exponential stability of periodic solution for a coupled system on networks with time delays

This paper investigates a type of coupled system on networks with time delays (CSND). By the combined method of graph theory, coincidence degree theory and Lyapunov function method, we establish sufficient conditions for the existence, uniqueness and global exponential stability of periodic solution of CSND. Moreover, the conditions we obtain are easy to be verified. Finally, we give a numerical example to illustrate the effectiveness of the results developed.