一类非线性动力系统混沌运动的研究

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基金项目: 国家自然科学基金;山西省留学回国人员基金

The Study on the Chaotic Motion of a Nonlinear Dynamic System

1.
Department of Mechanics, College of Traffic and Communications, South China University of Technology, Guangzhou 510641, P. R. China;
2.
Taiyuan University of Technology, Taiyuan 030024, P. R. China

摘要: 讨论了含二次和三次非线性项的受迫振动系统 -λ₁T+λ₂T²+λ₃T³=ε(gcosωt-ε'T)的混沌运动,利用Melnikov函数法给出了发生混沌的临界条件,结合相平面轨迹、时程曲线和Poincaré映射判定系统是否发生混沌.
- 混沌 /
- Melnikov函数法 /
- 相平面轨迹 /
- 时程曲线 /
- Poincaré映射
Abstract: In this paper the system of the forced vibration -λ₁T+λ₂T²+λ₃T³=ε(gcosωt-ε'T) is discussed, which contains square and cubic items. The critical condition that the systementers chaotic states is given by the Melnikov method. By Poincarmap, phase portrait and time-displacement history diagram, whether the chaos occurs is determined.
- chaos /
- Melnikov method /
- Poincar map /
- phase portrait /
- time-displacement diagram

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