具有非线性密度制约的HollingⅡ类功能性反应的食饵与捕食者模型的定性分析

Qualitative analysis for a kind of predator-prey model of HollingⅡ-function response with nonlinear density dependent

研究一类具有非线性密度制约的HollingⅡ型功能性反应的食饵-捕食者系统:x′=xg(x)-yφ(x),y′=y(-d+kφ(x))在g(x)=a-b x的情况下.分析了该系统的平衡点性态,证明了系统在正平衡点的外围极限环的存在性,得出了在一定的条件下,正平衡点外围至少有2或者3个极限环的结论.

A kind of predator - prey system of Holling Ⅱ - functional response with nonlinear density dependent x′=xg（x）-yφ（x）,y′=y（-d＋kφ（x）） is considered. This paper analyses the quality of the equilibrium point for this system on g（x）=a-b√x,φ（x）=ax/1＋ωx（a〉0,ω〉0） and a, b are positive. It obtains the conditions of the existence of limit cycle for this system and in certain conditions the number of limit cycles is at least 2 or 3.