Dynamic complexities of a food chain model with impulsive perturbations and Beddington–DeAngelis functional response

In this paper, the dynamic complexities of a three trophic level food chain system with impulsive perturbations and Beddington–DeAngelis functional responses is studied. Conditions for extinction of predator are given. By using the Floquet theory of impulsive equation and small amplitude perturbation skills, we consider the local stability of predator eradication periodic solution. Further, influences of the impulsive perturbation on the inherent oscillation are studied numerically, which shows the rich dynamics in the positive octant.