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We consider a delayed predator-prey model with harvesting effort and impulsive diffusion between two patches. By the impulsive comparison theorem and the discrete dynamical system determined by the stroboscopic map, we obtain some sufficient conditions on the existence and global attractiveness of predator-eradicated periodic solution for the system. Furthermore, the permanence of the system is derived. The obtained results will modify and improve the ones in some existing publications and give the estimate for the ultimately low and upper boundedness of the systems.

Dynamical Behaviors of a Stage-Structured Predator-Prey Model with Harvesting Effort and Impulsive Diffusion