The dynamical behaviors of the predator - prey model with stage structure and impulsive effects

In this paper, based on the theory of impulsive differential equations, we have studied a pre- dator-prey model with stage and impulsive effect. By use of the discrete dynamical system determined by the stroboscopic map, we obtain a predator-extinction´s periodicsolution and sufficient conditions of the global attractivity. By using the theory on delay functional and impulsive differ- ential equation, we obtain sufficient condition for the permanence of the system. Results are confirmed by numerical simulation.