一类比率依赖型捕食系统的稳定性分析

Stability Analysis of a Ratio-Dependent Predator-Prey System

研究了一类具有捕获项的比率依赖型捕食系统,讨论了系统正平衡点的存在性和各个平衡点的性态.它分析了非平凡正周期解的不存在性,构造lyaounov函数证明了该模型的正平衡点是全局稳定的结论,得到各个平衡点全局稳定性,并且研究捕食系统在各个平衡点下的最优收益,进而确定最优的捕获策略。

In recent years, some hot topics of ratio-dependent functional response predator-prey system are studied by people. In this paper, a ratio-dependent functional response predator-prey system include harvested item is researched. The existence of positive equilibrium point and properties of every equilibrium point are discussed. It proves condition that the model has no nontrivial positive periodic solution. By constructing Lyapunov function, the globally asymptotic stabilities of every equilibrium point are obtained. At the same time, the optimal harvested problems of every equilibrium point are studied, then it get the optimal harvest strategy of system.