一类具常数放养的非线性密度制约和功能反应的捕-食系统的定性分析

Qualitative analysis of a predator-prey system with constant-rate grazing prey species,nonlinear density dependence and functional response

利用微分方程定性理论研究一类具有常数放养的非线性密度制约和功能反应的捕-食模型,找出其平衡点存在的条件及局部稳定性态,同时给出正平衡点全局渐进稳定和存在唯一极限环的充分必要条件,并剖析其生物学意义.

Based on the qualitative theory of ordinary differential equations,it researched the predator-prey system with constan-trate grazing nonlinear density dependence and functional response,and found out the conditions for the existence of equilibrium point and the features of partial stability,simultaneously gave necessary and sufficient conditions for the gradually stability of overall situation and the existence of the unique positive equilibrium point,and its biological significance was explained.