Dynamics of a predator-prey system with pulses

In this paper, we investigate the dynamic behaviors of a Holling II two-prey one-predator system with impulsive effect concerning biological control and chemical control strategy-periodic releasing natural enemies and spraying pesticide at different fixed moment. By using the Floquet theory of linear periodic impulsive equation and small-amplitude perturbation method, we show that there exists a globally asymptotically stable two-prey eradication periodic solution when the impulsive period is less than some critical value. Further, we prove that the system is permanent if the impulsive period is larger than some critical value, and meanwhile the conditions for the extinction of one of the two-prey and permanence of the remaining two species are given. Finally, we give numerical simulation, with increasing of predation rate for the super competitor and impulsive period, the system displays complicated behaviors including a sequence of direct and inverse cascades of periodic-doubling, periodic-halving, chaos and symmetry breaking bifurcation. Our results suggest a new approach in the pest control.