| Summary: | Abstract The stability of coupled systems with time-varying coupling structure (CSTCS) is considered in this paper. The graph-theoretic method on a digraph with constant weight has been successfully generalized into a digraph with time-varying weight. In addition, we construct a global Lyapunov function for CSTCS. By using the graph theory and the Lyapunov method, a Lyapunov-type theorem and some sufficient criteria are obtained. Furthermore, the theoretical conclusions on CSTCS can successfully be applied to the predator-prey model with time-varying dispersal. Finally, a numerical example of CSTCS is given to illustrate the effectiveness and feasibility of our results.
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