具有Holling Ⅲ型功能反应捕食模型的稳定性及最优收获策略

摘要

A predator-prey model with Holling''s type Ⅲ functional response incorporating environmental control volume and tax is considered. Firstly, the existence of the positive equilibrium solution of the ODE system is discussed.Then, by the way of linear approximation, conditions are obtained for the local asymptotic stability of the positive equilibrium of the system. Next, global asymptotic stability of the equilibria is analyzed by constructing appropriate Lyapunov function. Finally, the system as an optimal control problem is transformed and the appropriate Hamilton function is established to derive an optimal economic equilibrium solution by the Pontryagin''s maximum principle.%研究了一个具有Holling Ⅲ型功能反应,且有环境控制量和税收的捕食-食饵系统.首先讨论该常微分系统的正平衡解的存在性.然后,通过线性近似的方法,得到正平衡解的局部渐近稳定性的条件;通过建立李雅普诺夫函数,得到正平衡解的全局渐近稳定性的条件.最后,将问题转化为最优控制问题,通过建立Hamilton函数,根据Pontryagin最大值原理求出一个最优经济平衡解.