A Pest Control Model with Periodic Coefficients and Impulses

In this paper, we consider a pest control model with natural enemy releases. The mathematical problem involves a predator-prey system with periodic coefficients and pulse conditions. First, we show that the system has a unique pest-free periodic solution, which is globally asymptotically stable under certain condition. Furthermore, we prove that the system is permanent if the pest-free periodic solution is unstable. The results generalize some conclusions in [8,9] for the system with constant coefficients. Some computer simulations are made to demonstrate the main results.