Abstract: Taking into account chemical control, biological control for pest management at different fixed moments, and the mutual interference of the predator, we propose in this paper a three-species predator-prey system with chemical control, biological control and mutual interference of predator. Based on the theory of impulsive equation, small amplitude perturbation and Floquet theory, we investigate the existence and globally asymptotic stability of the prey-eradication periodic solution for this system. By using comparison methods involving multiple Lyapunov functions, some sufficient conditions assuring the permanence of this system are obtained. Some examples and numerical simulations are given to show the complex behaviors of this system. Further, the biological implications of our main results are analyzed and some suggestions for feasible control strategies are given.

Key words: mutual interference, impulsive, extinction, permanence