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王万永, 陈丽娟 . 非线性时滞反馈对共振附近动力学行为的影响[J]. 信阳师范学院学报(自然科学版), 2014, 27(1): 15-18. DOI: 10.3969/j.issn.1003-0972.2014.01.005
引用本文: 王万永, 陈丽娟 . 非线性时滞反馈对共振附近动力学行为的影响[J]. 信阳师范学院学报(自然科学版), 2014, 27(1): 15-18. DOI: 10.3969/j.issn.1003-0972.2014.01.005
shu
Wang Wanyong , Chen Lijuan . Effects of Delayed Nonlinear Feedback on the Dynamics Near Resonance[J]. Journal of Xinyang Normal University (Natural Science Edition), 2014, 27(1): 15-18. DOI: 10.3969/j.issn.1003-0972.2014.01.005
Citation: Wang Wanyong , Chen Lijuan . Effects of Delayed Nonlinear Feedback on the Dynamics Near Resonance[J]. Journal of Xinyang Normal University (Natural Science Edition), 2014, 27(1): 15-18. DOI: 10.3969/j.issn.1003-0972.2014.01.005
shu

非线性时滞反馈对共振附近动力学行为的影响

Effects of Delayed Nonlinear Feedback on the Dynamics Near Resonance

    摘要
  • 摘要: 研究了一个具有线性和非线性时滞反馈的极限环振子系统1∶3共振双Hopf分岔.通过应用多尺度方法,得到了该1∶3共振的复振幅方程,并通过将其复振幅设为极坐标笛卡尔混合形式,将其复振幅方程转化为一个三维的实振幅系统.通过研究其实振幅方程,对系统在有非线性时滞反馈和无非线性时滞反馈两种情况下的动力学行为进行了分类和比较.结果显示,在两种情形下,系统有完全不同的动力学行为.

     

    Abstract: A 1∶3 resonant double Hopf bifurcation occurring in a limit cycle oscillator under time delayed linear and nonlinear feedbacks was studied. By using the method of multiple scales, the complex amplitude equations of 1∶3 resonance were obtained. By letting the complex amplitudes as a mixed polar Cartesian form, the complex amplitude equations were reduced to a three dimensional real amplitude equations. Then the dynamics around the 1∶3 resonant double Hopf bifurcation point was classified in two cases separately. Comparing the two classifications, it was found that there are completely different dynamics in two cases.

     

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