Periodic Solution of Prey‐Predator Model with Beddington‐DeAngelis Functional Response and Impulsive State Feedback Control

Abstract

A prey‐predator model with Beddington‐DeAngelis functional response and impulsive state feedback control is investigated. We obtain the sufficient conditions of the global asymptotical stability of the system without impulsive effects. By using the geometry theory of semicontinuous dynamic system and the method of successor function, we obtain the system with impulsive effects that has an order one periodic solution, and sufficient conditions for existence and stability of order one periodic solution are also obtained. Finally, numerical simulations are performed to illustrate our main results.