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

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Author:
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:
JOURNAL OF BIOMATHEMATICS
Issue:
Volume 25, Issue 04, 2010
DOI:
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.

  • [1]Goh B S.Management and Analysis of Biological Populations[M].Elsevier Scientific Publishing Company:Amsterdam,1980.
  • [2]Fan M,Wang K.Optimal harvesting policy for single population with periodic coefficients[J].Mathematical Biosciences,1998,152(2):165-177.
  • [3]Kot M.Elements of Mathematical Ecology[M].London:Cambridge University Press,2001.
  • [4]Clark C W.Mathematical Bioeconomics:the Optimal Management of Renewable Resources[M].New York:John Wiley and Sons,1976.
  • [5]Li Hailong.Logistic model for single-species with spatial diffusion and its optimal harvesting policy[J].Journal of Biomathematics,1993,14(03):293-300.
  • [6]LI Hai-yin,ZHANG Rui.Stability and optimal harvesting of a delayed ratio-dependent predator-prey system with stage structure[J].Journal of Biomathematics,2008,23(1):40-52.
  • [7]Zhang Jingru Chen Lansun.Periodic solutions of single-species nonautonomous diffusion models with continuous time delays[J].Mathematical and Computer Modelling,1996,23(7):17-27.
  • [8]ZhiXue Luo,Ze-Rong He.Optimal harvesting problem for an age-dependent n-dimensional competing system with diffusion[J].International Journal of Biomathematics,2008,2(1):133-145.
  • [9]Dong Lingzhen,Chen Lansun,Sun Lihua.Optimal harvesting policies for periodic Gompertz systems[J].Nonlinear Analysis:Real World Applications,2007,8(2):572-578.
  • [10]Dong Lingzhen,Chen Lansun,Shi Peilin.Periodic solutions for a two-species nonautonomous competition system with diffusion and impulses[J].Chaos,Solitons and Fractals,2007,32(5):1916-1926.
  • [11]Wang Limin,Liu Zhijun,Hui Jing,et al.Impulsive diffusion in single species model[J].Chaos,Solitons and Fractals,2007,33(4):1213-1219.
  • [12]Smith H L.Cooperative systems of differential equations with concave nonlinearities[J].Nonlinear Analysis.Theory,Methods & Applications,1986,10(10):1037-1052.
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