具有时滞耦合的<em>n</em>个van der Pol振子弱共振双Hopf分岔

王万永; 陈丽娟

doi:10.3879/j.issn.1000-0887.2013.07.012

具有时滞耦合的n个van der Pol振子弱共振双Hopf分岔

doi: 10.3879/j.issn.1000-0887.2013.07.012

河南工程学院理学院,郑州 451191

详细信息

作者简介:
王万永(1982—),男,河南南阳人,讲师,博士(通讯作者. E-mail:wangwanyong630@163.com).

中图分类号: O322;O175.1
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- 文章访问数: 1764
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- 被引次数: 0
出版历程
- 收稿日期: 2013-04-07
- 修回日期: 2013-05-25
- 刊出日期: 2013-07-15

Weak Resonant Double Hopf Bifurcation of n van der Pol Oscillators With Delay Coupling

College of Science, Henan Institute of Engineering, Zhengzhou 451191, P.R.China

摘要

摘要: 研究了具有时滞耦合的n个van der Pol振子系统中发生的弱共振双Hopf分岔．应用改进的多尺度方法，得到了2∶5共振的复振幅方程．通过将复振幅设为极坐标形式，将复振幅方程转化为一个二维的实振幅系统．通过研究实振幅方程的平衡点及其稳定性，对系统在2∶5共振点附近的动力学行为进行了开折和分类．得到了一些有趣的动力学现象，如振幅死区、周期解和双稳态解等，相应的数值模拟验证了理论结果的正确性．
- 双Hopf分岔 /
- 共振 /
- van der Pol振子 /
- 多尺度方法
Abstract: Weak resonant double Hopf bifurcation of nvan der Pol oscillators with delay coupling was investigated. With an extended method of multiple scales, the complex amplitude equations were obtained. With the complex amplitudes expressed in a polar form, the complex amplitude equations were reduced to a two dimensional real amplitude system. The equilibria and their stability of the real amplitud equations were studied, and the dynamics around 2∶5 resonant point unfolded and classified. Some interesting phenomena are found, such as amplitude death, periodic solution and bistability, etc. Validity of the analytical results is proved by their consistency with numerical simulations.
- double Hopf bifurcation /
- resonance /
- van der Pol oscillator /
- method of multiple scales

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参考文献(24)

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