Graph‐theoretic method on the periodicity of multipatch dispersal predator‐prey system with Holling type‐II functional response

Abstract

Holling type-II functional response in this paper. By providing a new method, we overcome the difficulty to get the priori bounds estimation of unknown solutions of operator equation Lu = Nu. Graph theory with coincidence degree theory is used, and a sufficient criterion for the periodicity of the system is obtained. The criterion presented in this paper is closely related with topological structure of dispersal network and can be verified easily. Finally, a numerical example is also provided to verify the effectiveness of theoretical results.

Global stability for a new predator–prey model with cross-dispersal among patches based on graph theory

“…However, the models presented in Refs. [1][2][3] were slightly different. One was to model and study multi-patch periodic predator-prey systems [1].…”

“…The dynamics of predator-prey models with self-dispersal have been studied by researchers in recent years. Many researchers devoted more time to discussing self-dispersal of prey, self-dispersal of predators and self-dispersal for both predators and prey of predator-prey models [1][2][3][4][5][6]. Self-dispersal of prey among n patches was considered in Refs.…”

“…Self-dispersal of prey among n patches was considered in Refs. [1][2][3]. However, the models presented in Refs.…”

“…Another was to consider multi-patch predator-prey systems without considering the periodic character [2]. The other was to study multipatch predator-prey systems with a Holling type-II functional response [3]. Predator-prey systems with self-dispersal of predators between two patches were studied in [4].…”