捕食者无密度制约的HollingⅢ型捕食系统的定性分析

Qualitative Analysis of Holling Ⅲ Predator-prey System without Density Restriction on Predators

研究食饵种群具有Logistic型密度制约但捕食者种群无密度制约的HolingⅢ型捕食系统,利用等倾线的基本性质,分析了正平衡点的存在性,通过构造Lyapunov函数给出了系统的全局渐近稳定性的充分条件,采用Bendixson环域定理和张芷芬极限环唯一性定理,证明了该系统在某一特定的条件下存在唯一稳定的极限环,最后利用Matlab通过数值模拟验证了理论分析的合理性.

In this paper,we study the predator-prey system of Holling Ⅲ with logistic density constraints but without density constraints of predator population.By using the basic properties of isocline,we analyze the existence of positive equilibrium points.By constructing Lyapunov function,we give sufficient conditions for the global asymptotic stability of the system.By using Bendixson’s ring field theorem and Zhang Zhengfen’s limit cycle uniqueness theorem,we prove that the system has a unique stable limit cycle under certain conditions.Finally,the rationality of the theoretical analysis in this paper is verified by numerical simulation using Matlab.