mathematical model of a three species prey-predator system with impulsive control and Holling functional response

In this paper, we investigate a three species prey-predator system with impulsive prey harvest and Holling type II functional response. By using Floquet’s Theorem and the small amplitude perturbation method, we obtain that there exists an asymptotically stable preys-eradication periodic solution when the impulsive period is less than some critical minimum value (or the release amount of the predator is larger than some critical maximum value), and the system is permanent under the conditions that both the death rate and impulsive period are grater than some critical maximum values. The results indicate that the a large death rate and a long impulsive period will lead the system permanent. Numerical results show that the system we considered has more complex dynamics.