| 摘要: |
| 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。 |
| 关键词: Lienard方程 Hopf分支 稳定性 时滞微分方程 滞量 中心流形 规范型理论 分支周期 数值计算 |
| DOI：10.11841/j.issn.1007-4333.2003.04.093 |
| 修订日期：2002-12-30 |
| 基金项目:国家自然科学基金资助 (No .10 172 0 11) |
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| Hopf bifurcation of a lienard differential equation with delay |
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| Abstract: |
| 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. |
| Key words: delay,Hopf bifurcation,Lienard differential equation, |
