具有平方、立方非线性项的耦合动力学系统1:2内共振分岔

基金项目: 国家重点基础研究专项经费资助(G1998020316);国家自然科学基金资助项目(19990510);教育部博士点基金资助项目(D09901)

1:2 Internal Resonance of Coupled Dynamic System With Quadratic and Cubic Nonlinearities

摘要: 对一类具有平方、立方非线性项的耦合动力学系统1:2内共振情形进行了研究.首先,用直接方法求出该系统1:2内共振时的Normal Form,该系统的Normal Form中,不仅含有平方非线性项,同时还含有立方非线性项.通过采用适当的变量变换,将4维分岔方程约化成3维,进而得到单变量4次分岔方程.最后用奇异性理论,研究了一类普适开折的分岔特性.该方法可用于4维中心流形上流的强内共振时的分岔行为分析.
- 平方立方非线性 /
- NormalForm /
- 1:2内共振分岔
Abstract: The 1:2 internal resonance of coupled dynamic system with quadratic and cubic nonlinearities is studied.The normal forms of this system in 1:2 internal resonance were derived by using the direct method of normal form.In the normal forms,quadratic and cubic nonlinearities were remained.Based on a new convenient transformation technique,the 4-dimension bifurcation equations were reduced to 3-dimension.A bifurcation equation with one-dimension was obtained.Then the bi furcation behaviors of a universal unfolding were studied by using the singularity theory.The method of this paper can be applied to analyze the bifurcation behavior in strong internal resonance on 4-dimension center manifolds.
- quadratic and cubic nonlinearities /
- Normal Form /
- 1:2 internal resonance

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