环境污染下基于最优捕获策略的近海-远海捕鱼模型的动力学性质(英文)  

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

作　　者：康宝林[1] 刘兵[2] 马毅[3] 

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029 [2]鞍山师范学院数学系,辽宁鞍山114007 [3]沈阳大学科学学院,辽宁沈阳110044

出　　处：《生物数学学报》2010年第4期583-592,共10页Journal of Biomathematics

基　　金：Supported by National Natural Science Foundation of China(10971001, 10671001);is also supported by Excellent Staffs Support Project of Universities and Colleges in Liaoning

摘　　要：近年来,由于人类的过度开发,使得海洋资源(尤其是近海海洋资源)急剧下降,加上日益严重的海洋污染,给海洋资源管理带来很大的困难.为了更好的管理和利用海洋资源,本文考虑到环境污染中脉冲扩散对种群的影响,建立了一个近海-远海渔业模型,给出了正周期解存在性及平凡周期解和正周期解全局渐近稳定性的充分条件.进一步,在环境污染的情况下,给出了最优捕获策略,得到了最大持续产量和相应的捕获努力量.最后,通过数值模拟证实了我们所得的结论的正确性.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 inshore-offshore 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.

关 键 词：污染 脉冲扩散 近海-远海渔业模型 全局渐近稳定性 周期解 最优捕获策略 

分 类 号：O175.12[理学—数学]