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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.