一类具Holling Ⅱ型双密度制约捕食系统的定性分析

Qualitative analysis of a class of Holling Ⅱ predator-prey system with double density restriction

研究了一类食饵具有非线性密度制约且捕食者具有线性密度制约的Holling Ⅱ型捕食系统,得到了系统正平衡点的存在性条件.利用构造的Lyapunov函数给出了正平衡点全局渐近稳定性的充分条件,并得到了系统极限环的存在唯一性条件.

This paper studies a class of Holling II predator-prey system which the prey is nonlinear density restricted and the predator is linear density restricted, the existence condition of the system positive equilibrium point is obtained. This paper gives the sufficient condition of the positive equilibrium point global asymptoic stability by constructing Lyapunov function and obtains the existence and uniqueness condition of the system limit cycle.