Study Of A Predator-prey Model With Stage Structure And Pulse Diffusion

In this article, we discuss a stage-structured predator-prey model with diffusion. The population of prey spread arbitrarily between two patches while the population of predator stay in one patch. We first prove that all solutions of the system are uniformly ultimately bounded.Using the stroboscopic map of the discrete dynamical system,we obtain the sufficient condition of the globally attractive condition of predator-extinction periodic solution of the system. By the theory on the delay and impulsive differential equation,we prove that the investigated system is permanent. Our results indicate that the discrete time delay has influence to the dynamical behaviors of the system.