Synchronization of multi-group coupled systems on networks with reaction-diffusion terms based on the graph-theoretic approach

In this paper, we present mainly the analysis of synchronization of multi-group coupled systems on networks with reaction-diffusion terms (MCSNRTs). Specially, we provide a novel graph-theoretic approach which is very helpful in the respect of constructing a global Lyapunov function. Then, based on graph-theoretic approach and Lyapunov method, two kinds of sufficient criteria that one is Lyapunov-type theorem and the other is coefficient-type theorem are acquired to guarantee the synchronization of MCSNRTs. Finally, a numerical example is offered to demonstrate the practicability and effectiveness of our main results.