摘要
研究了同一鱼类种群同时分布于保护区斑块和非保护区斑块,且鱼群密度服从Gompertz增长的生物经济系统.首先,证明了系统内存在唯一的非平凡奇点并且局部稳定,运用Bendixson-Dulac定理得到该奇点的全局稳定性;然后,通过Pontryagin最大值原理获得该鱼类种群的最优捕捞路径;最后,通过数值模拟来说明部分结论.
In order to protect the population on the verge of extinction and sustain the biodiversity of marine ecosystem,marine protected area(MPA)is established to provide a refuge for fishery resource.However,the influence of current harvesting policy on the MPA is still poorly understood.We consider a bioeconomic Gompertz population model in a two-patch environment:a free fishing zone and a protected zone where fishing is strictly prohibited.First,we have proved the existence of the equilibrium in which it is also local stable.In virtue of Bendixson-dulac theorem,the global stability of the nontrivial steady state is obtained.Then,the optimal harvesting policy is established by use of Pontryagin's maximum principle.In the final,the results are illustrated with the help of some numerical examples.
引文
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