Stability analysis of discrete-time multi-patch Beddington–DeAngelis type predator-prey model with time-varying delay

This paper is concerned with the stability of a discrete-time multi-patch Beddington–DeAngelis type predator-prey model with time-varying delay, where the dispersal of both predators and prey is considered. A nonstandard finite difference scheme is used to discretize this model. Then, combining the Lyapunov–Krasovskii method with the graph-theoretical technique, a stability criterion is derived, which is closely related to the dispersal topology. And an example with numerical simulation is given to demonstrate the effectiveness of the obtained results.