具Holling Ⅱ功能反应的捕食系统的稳定性与最优收获策略问题

Stability and Optimal Harvesting Policy of Predator-prey System with Holling Ⅱ Function Response

运用微分方程理论对具有Holling Ⅱ功能反应的捕食系统进行研究.在适当的假设条件下,采用Routh-Hurwitz判别法证明了系统正平衡点是局部渐进稳定的,通过构造Liapunov函数证明了系统正平衡点是全局渐进稳定的,同时应用Pantryagin’s最大值原理给出了资源种群可持续生存的最优收获策略.

The Predator-prey System with Holling II function response was studied by using the theory of differential equation. Under appropriate assumption, the locally asymptotical stabilty of system＇s positive equilibrium was proved by applying Routh-Hurwitz criterion, the globally asymptoticical stability of the positive equilibrium was proved by constructing a Liapunov function and the optimal harvesting policy for permanence of resource stock was obtained by applying Pantryagin＇s Maximum Principle.