非线性振动系统的异宿轨道分叉、次谐分叉和混沌

张伟; 霍拳忠; 李骊

非线性振动系统的异宿轨道分叉、次谐分叉和混沌

1.
天津大学力学系;
2.
北京工业大学

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出版历程
- 收稿日期: 1991-01-21
- 刊出日期: 1992-03-15

Heteroclinic Orbit and Subharmonic Bifurcations and Chaos of Nonlinear Oscillator

1.
Tianjin University, Tianjin;
2.
Beijing Polytechnic University, Beijing

摘要

摘要: 在参数激励与强迫激励联合作用下具有van der Pol阻尼的非线性振动系统,其动态行为是非常复杂的.本文利用Melnikov方法研究了这类系统的异宿轨道分叉、次谐分叉和混沌.对于各种不同的共振情况,系统将经过无限次奇阶次谐分叉产生Smale马蹄而进入混沌状态.最后我们利用数值计算方法研究了这类系统的混沌运动.所得结果揭示了一些新的现象.
- 异宿轨道分叉 /
- 次谐分叉 /
- 混沌运动 /
- 参数激励 /
- Melnikov方法
Abstract: Dynamical behavior of nonlinear oscillator under combined parametric and forcing excitation, which includes yon der Pol damping, is very complex. In this paper, Melnikov's method is used to study the heteroclinic orbit bifurcations, subharmonic bifurcations and chaos in this system. Smale horseshoes and chaotic motions can occur from odd subharmonic bifurcation of infinite order in this system-far various resonant cases finally the numerical computing method is used to study chaotic motions of this system. The results achieved reveal some new phenomena.
- heteroclinic orbit bifurcations /
- subharmonic bifurcations /
- chaotic motions /
- parametric excitation /
- Melnikov’s method

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参考文献(13)

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