具有Holling-Ⅱ型功能反应函数的双时滞捕食者-食饵系统的Hopf分支

Hopf bifurcation of a predator-prey system with two delays and Holling-II functional response function

在具有Holling-Ⅱ型功能反应函数的捕食者-食饵系统中引入2个时滞参数,用来刻画捕食者和食饵的生长时滞,研究了系统平衡点的局部稳定性.结果表明,随着参数的变化,系统平衡点发生了扰动,进而出现了周期解.给出了Hopf分支存在条件的显示表达式,并通过数值实验验证了结论.

Two time-delay parameters are introduced into a predator-prey system with Holling-Ⅱfunctional response function,they are used to describe the growth delay of predators and prey.The local stability of the equilibrium of the system was analyzed,the results exhibited that the equilibrium point of the system is disturbed,and then a periodic solution appears with the change of parameters.The explicit algorithms for Hopf bifurcation are derived,the conclusion is verified by numerical experiments.