Existence of Stable Periodic Orbits for a Predatory-Prey Model with Deddington-DeAngelis Functional Response and Delay

Abstract

In this paper a Beddington-DeAngelis predator-prey model with time lag for predator is proposed and analyzed. Mathematical analysis regard to boundedness of solutions, nature of equilibria, uniform persistence, and stability are analyzed. We show that if the positive equilibrium is unstable, an orbitally asymptotically stable periodic solution exists.