一类具有时滞的Lienard方程的Hopf分支

Hopf bifurcation of a lienard differential equation with delay

研究了一类时滞Lienard方程的稳定性及其Hopf分支问题。以滞量作为参数 ,分析了方程的零解的稳定性 ,得到了Hopf分支值 ;应用中心流形和规范型理论 ,得到了确定Hopf分支方向和分支周期解稳定性的计算公式。给出了一个具体的超临界Hopf分岔的例子 ,表明理论分析和数值计算结果具有一致性。

A Lienard differential equation with time-delay is studied. The time delay r can qualitatively change the dynamics. Choosing time delay r as parameter, when r increases, the unique equilibrium can switch from being stable to unstable, thus Hopf bifurcation happens. The bifurcation direction is also computed by using the normal form method.