具有食饵避难的Leslie-Gower捕食系统最优收获分析

研究了一类具有食饵避难的Leslie-Gower捕食与被捕食系统收获模型,利用Hurwitz判据,得到了正平衡点局部渐近稳定,进一步构造了适当的Lyapunov函数,证明了正平衡点的全局渐近稳定性.并且在捕获努力量假说下,对发生食饵避难的两种群同时捕获,考虑了生态经济平衡点的存在性和利用Pontryagin最大值原理对两种群进行最优收获,得到当贴现率为零时,既保持了生态平衡,又使得在渔业开发过程中取得最大经济利益.

Analysis of a Harvested Leslie-Gower Predator-Prey Model Incorporating a Prey Refuge

In this paper,we analyze and formulate a harvested Leslie-Gower predator-prey model incorporating a prey refuge,both the population are harvested where we use the usual Catch-per-unit-effort hypothesis.We study the existence of the non-negative equilibria,obtain the sufficient conditions of locally asymptotically stable of the equilibria by the Hurwitz criterion,then we analyze the global stability of the equilibria by constructing appropriate Lyapunov functions.The existence of bionomic equilibria is established.Next,the optimal harvesting policy is discussed.The present value of revenues is maximized by using Pontryagin's maximal principle.lt is established that the zero discounting leads to the maximization of economic revenue.