Global stability analysis for discrete-time coupled systems with both time delay and multiple dispersal and its application

This paper is concerned with the global stability analysis of discrete-time coupled systems with both time delay and multiple dispersal (DCSTMs). We provide a systematic method to constructing a global Lyapunov function for DCSTMs. By employing the graph-theoretic method on multiple digraphs and Lyapunov method, a Lyapunov-type theorem and a coefficients-type criterion for a DCSTM are derived to guarantee global stability for the DCSTM. The main results are applied to a discrete-time predator-prey model with time delay where both preys and predators disperse among l patches, which is discretized by a nonstandard finite difference scheme. A numerical example is provided to show the effectiveness of the proposed results.