一类具有功能反应的食饵-捕食模型的定性分析

Qualitative Analysis of Class of Predator-Prey Model with Functional Response

研究一类具有功能反应的食饵-捕食者系统平衡点及极限环的定性行为,得到正平衡点的稳定性,并且利用Dulac函数讨论极限环的存在性,得到此系统没有极限环的结论,进一步获得食饵种群密度与捕食者种群密度的依赖关系。

This paper studies qualitative behavior of positive equilibrium and limit cycle of a class of two species predator-prey model with functional response to obtain the stability of positive equilibrium, discusses the existence of limit cycle by using Dulac function, and reaches the conclusion of nonexistence of limit cycle. Finally, the dependent relationship between predator species density and prey species density is obtained.