具有Michaelis-Menten功能反应捕食系统的征税模型

Taxation Model of Prey-predator with Michaelis-Menten Functional Response

研究了一类具有Michaelis-Menten功能反应捕食系统的征税模型,对收获函数进行了更合理的修正.讨论了该系统的平衡点的性态,得到正平衡点的局部渐近稳定性和全局渐近稳定性的充分条件,利用Pontrjagin最大值原理得到了最优税收策略.最后通过计算机模拟,验证了其平衡点稳定性和最优税收策略的理论结果.

A prey-predator system with Michaelis-Menten functional response and taxation is researched. It uses a reasonable catch-rate function instead of the usual catch-per-effort hypotheses. We study-the existence of its steady state. The sufficient condition of the local and global asymptotic stability are investigated. By using Pontrjagin＇ s maximum principle, we obtain the optimal taxation policy. Finally, the theoretical results on the stabilities of the equilibrium points and the optimal taxation policy are verified by using the simulation of computer.