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Extinction and permanence of the predator-prey system with stocking of prey and harvesting of predator impulsively. (English) Zbl 1086.92051
Summary: A predator-prey system with stocking of prey and harvesting of predator impulsively is studied. Here, the prey population is stocked with a constant quantity and the predator population is harvested at a rate proportional to the species itself at fixed moments. Under some conditions, the existence and global asymptotic stability of the boundary periodic solution are proved, which implies that the system will be extinct; and given some different restrictions, ultimate positive upper and lower bounds of all solutions are obtained, showing the system being permanent. At last, two examples are given to illustrate our results.

MSC:
92D40 Ecology
34C25 Periodic solutions to ordinary differential equations
34D23 Global stability of solutions to ordinary differential equations
34A37 Ordinary differential equations with impulses
34D05 Asymptotic properties of solutions to ordinary differential equations
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