中文摘要：

研究一类具有Michaelis-Menten收获率的Holling-III类功能性捕食者-食饵征税模型,利用微分方程定性理论,讨论正平衡点的局部渐近稳定性,通过构造Lyapunov函数,给出正平衡点全局渐近稳定性的充分条件。利用Pontryagain最大值原理,确定最优征税策略。用Matlab软件进行模拟,验证了正平衡点稳定性和最优税收策略的理论结果。

英文摘要：

Consider a class of prey-predator model with taxation and Michaelis-Menten harvesting rate un- der Holling-III functional response. The local asymptotic stability of the positive equilibrium point is dis- cussed firstly in the terms of the stability theory of differential equations. Secondly, the sufficient condi- tion of global asymptotic stability of the positive equilibrium point is given by constructing Lyapunov func- tion. At the same time, an optimal taxation policy is obtained by Pontryagain＇ s maximum principle. Fi- nally, the theoretical results on the stability of the positive equilibrium point and the optimal taxation poli- cy are verified by Matlab simulation.