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Extinction and permanence of the predator–prey system with stocking of prey and harvesting of predator impulsively

✍ Scribed by Lingzhen Dong; Lansun Chen; Lihua Sun

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
112 KB
Volume
29
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

In this paper, 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. Copyright © 2005 John Wiley & Sons, Ltd.

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