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, |