非线性时滞反馈对共振附近动力学行为的影响

基金项目:

国家自然科学基金项目(11302072)

河南工程学院博士基金项目(D2012021)

详细信息

Effects of Delayed Nonlinear Feedback on the Dynamics Near Resonance

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.
- 时滞 /
- 双Hopf分岔 /
- 共振 /
- 极限环振子 /
- 多尺度方法
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.
- time delay /
- double Hopf bifurcation /
- resonance /
- limit cycle oscillator /
- the method of multiple scales

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