Dynamics of Inshore-Offshore Fishery Model Concerning Optimal Harvesting Policy in a Polluted Environment

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KANG Bao-lin(Department of Mathematics, Liaoning Normal University, Dalian Liaoning 116029 China)
LIU Bing(Department of Mathematics, Anshan Normal University, Anshan Liaoning 114007 China)
MA Yi(College of Science, Shenyang University, Shenyang Liaoning 110044 China)
Journal Title:
Volume 25, Issue 04, 2010
Key Word:
Pollution;Impulsive diffusion;Inshore-offshore fishery model;Global asymptotic stability;Periodic solution;Optimal harvesting policy

Abstract: Recently, due to excessive exploitation of marine resources, the ocean resources extremely decline. More and more serious marine pollution (especially inshore marine pollution) brings great difficulty for marine resources management. In order to better manage and utilize the marine resources, in this paper, we consider the effects of impulsive diffusion on the species in a polluted environment and investigate an inshoreoffshore fishery model. The sufficient conditions are obtained for the existence of the positive periodic solution and the global asymptotic stability of both the trivial periodic solution and the positive periodic solution. Moreover, in a polluted environment,the optimal harvesting policy is given for the inshore subpopulation, which includes the maximum sustainable yield and the corresponding harvesting effort. Numerical simulations confirm our theoretical results.

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