Chaos in three species food chain system with impulsive perturbations

In this paper, we investigate three species food chain system with periodic constant impulsive perturbations of mid-level predator. Conditions for extinction of lowest-level prey and top predator are given. By using the Floquet theory of impulsive equation and small amplitude perturbation skills, we consider the local stability of lowest-level prey and top predator eradication periodic solution. Further, influences of the impulsive perturbations on the inherent oscillation are studied numerically, which shows the rich dynamics (for example: period doubling, period halfing, non-unique dynamics) in the positive octant. The dynamics behavior is found to be very sensitive to the parameter values and initial value.