中文摘要：

研究一类具有多时滞三种群食物链系统,其中食饵具有密度制约,且捕食者对二级食饵的作用是非线性的HollingⅡ类功能反应函数。利用霍尔维茨判别法给出系统正平衡点为局部稳定的条件,以滞量τ为参数,利用Hopf分支理论给出系统在正平衡点处存在Hopf分支的充分条件。利用Matlab进行了数值模拟。

英文摘要：

A food chain model with time delays and Holling Ⅱ functional response is studied in this paper, which prey has density-dependant. Through Hurwitz criterion, sufficient conditions for the local as- ymptotic stability of the positive equilibrium are given. And by using Hopf bifurcation theorems, the existence of Hopf bifurcation on the positive equilibrium is discussed. Finally, numerical simulations are carried out to illustrate these conclusions.