耦合Vander Pol-Duffing振子的强共振分叉解

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基金项目: 国家自然科学基金(19872010);国家教委博士点基金(98B51125);航空科学基金(98B51125)

Strongly Resonant Bifurcations of Nonlinearly Coupled Van der Pol-Duffing Oscillator

Department of Applied Mathematics and Physics, Beijing University of Aeronautics and Astronautics, Beijing 100083, P R China

摘要: 本文用多尺度方法研究了一非线性耦合Vander Pol-Dufing振子在强共振情形下的分叉解。研究表明,当分叉参数取不同值时,此系统将出现单个振子的周期运动、两个振子的锁频分叉运动和拟周期分叉运动,同时,本文也给出一些数值结果,以验证理论的正确性。
- 非线性耦合 /
- 多尺度法 /
- 锁频 /
- 拟周期
Abstract: In this paper, the strongly resonant bifurcations of a nonlinear coupled Van der Pol-Duffing Oscillator by the classical multi-scale method are studied. It is shown that there exit periodic motions of a single oscillator,frequency-locking and quasi-periodic motions of two oscillators when the parameters vary. Meanwhile, some numerical results are given to test the theoretical ones.
- non-linearly coupling /
- multi-scale method /
- frequency-locking /
- quasi-periodic

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