Bifurcation of nontrivial periodic solutions for a Beddington–DeAngelis interference model with impulsive biological control

Abstract

In this paper, a Beddington–DeAngelis interference model with impulsive biological control is studied. The pest-free periodic solution is local asymptotically stable if the impulsive control rate is larger than a critical value or the release period is smaller than another critical value. Conditions for permanence of the model are established. The existence of nontrivial periodic solution is established when the pest-free periodic solution loses its stability.