Global stability of periodic solutions for a discrete predator-prey system with functional response

The purpose of this paper is to study the existence and global stability of a periodic solution for a discrete predator-prey system with the Beddington-DeAngelis functional response and predator cannibalism. By using the continuation theorem, the existence conditions of at least one periodic solution are obtained, and the sufficient conditions, which ensure the global stability of the positive periodic solution, are derived by constructing a special Lyapunov function.