A Study of the Static and Global Bifurcations for Duffing Equation
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摘要: 对于Duffing方程的静态和全局动态分岔,通过研究平均方程的全局行为得到了出现各种分岔的条件,揭示了Duffing方程周期解的变化过程及其具有的非线性动力学性质。Abstract: In this paper,the static and global bifurcations of the forced Duffing equation have been studied by means of the averaged system.Bifurcation condition has been obtained in the whole parametric space.The change of the phase plane structure has been investigated.
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Key words:
- ored Duffing equation /
- averaged system /
- bifurcation
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[1] Holmes P J,Rand D A.The bifurcations of Duffings'equation: an application of catastrophe theory[J].J Sound and Vibration,1976,44(2):237~253. [2] 陈予恕,非线性振动系统的分岔和浑沌理论[M].北京:高等教育出版社,1993. [3] Guckenheimer J,Holmes P.Nonlinear Oscillations,Dynamics,and Bifurcations of Vector Fields[M].New York,Berlin,Heidelberg,Tokyo: Springer-Verlag,1983. [4] Golubitsky M,Schaeffer D G.Singularities and Groups in Bifurcation Theory[M].New York,Berlin,Heidelberg,Tokyo: Springer-Verlag,1984.
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