具Holling Ⅱ类功能反应函数的食饵-捕食系统的定性分析

Qualitative Analysis of Two Species Predator-prey Systems with Holling’s Type Ⅱ Functional Response

研究具有非线性密度制约的Holling II型功能反应的食饵-捕食两种群模型,讨论了该系统的非负平衡点性态和其对应的反映扩散系统正平衡点的稳定性,最后证明了系统在平衡点外围至少存在一个稳定极限环.

This paper studied two types of group models of species predator-prey of Holling＇s type Ⅱ functional response with nonlinear density dependent. The quality of the nonnegative equilibrium point for this system and the stability of positive equilibrium point for its reaction-diffusion system were analyzed. At the end of this paper, we can easily draw a conclusion that at least one limit cycle for the ODE system does exist.