一类食饵种群具有常数收获率的Holling-IV类功能性反应的捕食系统的定性分析

The qualitative analysis of a predator-prey system with constant-rate prey harvesting under type-IV functional response

研究一类食饵种群具有常数收获率的Holling-IV类功能性反应的捕食系统:dxdt=x(a-bx-cx2)-βx+yx2-hdydt=y-d+βμ+xx2在4βd2<μ2≤469βd2,Φ(x2)>0,x1<x1<x2<x2情形下系统极限环的存在情况,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.得到了在一定条件下,正平衡点外围至少存在2个极限环的结论.

A class of a predator - prey system with constant - rate prey harvesting under type - Ⅳ functional response is investigated：dxdt=x（a-bx-cx2）-βx＋yx2-hdydt=y-d＋βμ＋xx2We study the quality of the equilibria of the system and prove the existence of limit cycles around the positive equilibra under the condition of 4βd2〈μ2≤469βd2,Φ（x2）〉0,and x1^-〈x1^=〈x2^-〈x2^= We also abtain the result that the system has two limit cycles under some given conditions.