Dynamics of an $n$-Patch Predator-Prey Model with Allee Effect

Abstract

A class of $n$-patch predator-prey diffusion models with the Allee effect is established. The influence of the Allee effect and diffusion of prey on the existence and stability of the equilibrium point are investigated. Firstly, sufficient conditions for the permanence and extinction of the system are analyzed. Secondly, by constructing a new Lyapunov function in terms of graph theory, we obtain a sufficient condition of the global asymptotical stability for the positive equilibrium point. Finally, our results of this paper are verified by Matlab simulation.