Permanence in a food chain system with impulsive perturbations

In this article, we investigate three species food chain system with Holling II functional responses and periodic constant impulsive perturbations of predator at different fixed time. The conditions for extinction of prey and top predator are given. By using the Floquet theory of impulsive differential equation and small amplitude perturbation skills, we consider the local stability of prey and top predator eradication periodic solution. Further, we obtain the conditions of permanence of the system. The complex dynamics behavior of the system (1.3) is found by using numerical method.