Survival analysis for a periodic predator–prey model with prey impulsively unilateral diffusion in two patches

Abstract In this paper, we study a periodic predator–prey system with prey impulsively unilateral diffusion in two patches. Firstly, based on the results in [41] , sufficient conditions on the existence, uniqueness and globally attractiveness of periodic solution for predator-free and prey-free systems are presented. Secondly, by using comparison theorem of impulsive differential equation and other analysis methods, sufficient and necessary conditions on the permanence and extinction of prey species x with predator have other food source are established. Finally, the theoretical results both for non-autonomous system and corresponding autonomous system are confirmed by numerical simulations, from which we can see some interesting phenomena happen.

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