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Extinction and permanence of the predator–prey system with stocking of prey and harvesting of predator impulsively
Author(s) -
Dong Lingzhen,
Chen Lansun,
Sun Lihua
Publication year - 2005
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.688
Subject(s) - mathematics , predation , predator , extinction (optical mineralogy) , stocking , population , control theory (sociology) , ecology , biology , fishery , economics , paleontology , demography , control (management) , management , sociology
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.