双时滞Holling型捕食-食饵系统的Hopf分支

Hopf Bifurcation Analysis of Holling Type Predator-Prey Model with Two Time Delay

研究了一类具有双时滞的Holling型捕食-食饵模型.讨论了该系统的正平衡点的局部稳定性以及Hopf分支存在的充分条件.利用中心流形定理和规范型理论,得出确定该系统Hopf分支方向和分支周期解稳定性的计算公式.最后,运用数值模拟验证结论.

A predator-prey model with time delay is examined in this work. By analyzing the characteristic equations,we discussed the local stability of equilibria of the system and established the existence of Hopf bifurcation at the coexistence equilibrium. By choosing the delay as a bifurcation parameter,we can determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions by using the nomal form theory and center manifold argument. Numerical simulations were carried out to illustrate the main results of this work.