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In this paper, we consider a predator-prey model with prey impulsive diffusion and dispersal delay. By utilizing the dynamical properties of a single-species model with diffusion and dispersal delay between two patches and the comparison principle of impulsive differential equations, we establish the sufficient conditions on the global attractivity of predator-extinction periodic solution and the permanence of species for the model.

Dynamical behaviors of a predator-prey system with prey impulsive diffusion and dispersal delay between two patches