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Study on harvested population with diffusional migration. (English) Zbl 0976.92023

Summary: This paper is devoted to the study of the dynamical behavior and harvesting problem of an exploited population with diffusional migration, for which a protective patch is established. We examine the effects of protective patch and harvest on the population resources and conclude that the protective patch is effective for the conservation of population resources and ecological environment, though in some cases the extinction can not be eliminated.

The dangerous region, the parameters domains and the typical bifurcation curves of stability of steady states for the considered system are determined. The optimal harvest policy for the considered population is made also. The explicit expressions are obtained for the optimal harvesting effort, the maximum sustainable yield and the corresponding population density. Our results provide a theoretical evidence for the practical management of biological resources.

MSC:
92D40Ecology
34D05Asymptotic stability of ODE
37N25Dynamical systems in biology
34D23Global stability of ODE