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

Taking into account periodic impulsive biological and chemical control for pest management at different fixed moment, a three species prey-predator system with Holling type II functional response was investigated. By using Floquet's theory and the small amplitude perturbation method, it was obtained 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 insecticidal effect and impulsive period are grater than some critical maximum values. Furthermore, it is obtained that IPM is more effective than any single one after comparison. Finally, numerical simulations are carried on to show the complex dynamic behavior of system.