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参数激励Duffing-VanderPol振子的动力学响应及反馈控制

李欣业 陈予恕 吴志强 宋涛

李欣业, 陈予恕, 吴志强, 宋涛. 参数激励Duffing-VanderPol振子的动力学响应及反馈控制[J]. 应用数学和力学, 2006, 27(12): 1387-1396.
引用本文: 李欣业, 陈予恕, 吴志强, 宋涛. 参数激励Duffing-VanderPol振子的动力学响应及反馈控制[J]. 应用数学和力学, 2006, 27(12): 1387-1396.
LI Xin-ye, CHEN Yu-shu, WU Zhi-qiang, SONG Tao. Response of a Parametrically Excited Duffing-Van der Pol Oscillator With Delayed Feedback[J]. Applied Mathematics and Mechanics, 2006, 27(12): 1387-1396.
Citation: LI Xin-ye, CHEN Yu-shu, WU Zhi-qiang, SONG Tao. Response of a Parametrically Excited Duffing-Van der Pol Oscillator With Delayed Feedback[J]. Applied Mathematics and Mechanics, 2006, 27(12): 1387-1396.

参数激励Duffing-VanderPol振子的动力学响应及反馈控制

基金项目: 教育部留学回国人员科研启动基金资助项目(教外司留[2006]331号)
详细信息
    作者简介:

    李欣业(1966- ),男,河北唐山人,博士,副教授(联系人.Tel:+86-22-26582769;E-mail:xinyeli@eyou.com).

  • 中图分类号: O323

Response of a Parametrically Excited Duffing-Van der Pol Oscillator With Delayed Feedback

  • 摘要: 研究了Duffing-Van der Pol振子的主参数共振响应及其时滞反馈控制问题.依平均法和对时滞反馈控制项Taylor展开的截断得到的平均方程表明,除参数激励的幅值和频率外,零解的稳定性只与原方程中线性项的系数和线性反馈有关,但周期解的稳定性还与原方程中非线性项的系数和非线性反馈有关.通过调整反馈增益和时滞,可以使不稳定的零解变得稳定.非零周期解可能通过鞍结分岔和Hopf分岔失去稳定性,但选择合适的反馈增益和时滞,可以避免鞍结分岔和Hopf分岔的发生.数值仿真的结果验证了理论分析的正确性.
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出版历程
  • 收稿日期:  2005-07-02
  • 修回日期:  2006-07-24
  • 刊出日期:  2006-12-15

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