中国物理B ›› 2002, Vol. 11 ›› Issue (10): 1004-1007.doi: 10.1088/1009-1963/11/10/306

• GENERAL • 上一篇    下一篇

Bifurcations of a parametrically excited oscillator with strong nonlinearity

唐驾时1, 符文彬1, 李克安2   

  1. (1)Department of Mechanics, Hunan University, Changsha 410082, China; (2)Yueyang Normal College, Yueyang 411400, China
  • 收稿日期:2002-04-16 修回日期:2002-05-29 出版日期:2005-06-12 发布日期:2005-06-12
  • 基金资助:
    Project supported by the Natural Science Foundation of Hunan Province, China (Grant No 011JJY2007).

Bifurcations of a parametrically excited oscillator with strong nonlinearity

Tang Jia-Shi (唐驾时)a, Fu Wen-Bin (符文彬)a, Li Ke-An (李克安)b   

  1. a Department of Mechanics, Hunan University, Changsha 410082, China; b Yueyang Normal College, Yueyang 411400, China
  • Received:2002-04-16 Revised:2002-05-29 Online:2005-06-12 Published:2005-06-12
  • Supported by:
    Project supported by the Natural Science Foundation of Hunan Province, China (Grant No 011JJY2007).

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摘要： A parametrically excited oscillator with strong nonlinearity, including van der Pol and Duffing types, is studied for static bifurcations. The applicable range of the modified Lindstedt－Poincaré method is extended to 1/2 subharmonic resonance systems. The bifurcation equation of a strongly nonlinear oscillator, which is transformed into a small parameter system, is determined by the multiple scales method. On the basis of the singularity theory, the transition set and the bifurcation diagram in various regions of the parameter plane are analysed.

Abstract: A parametrically excited oscillator with strong nonlinearity, including van der Pol and Duffing types, is studied for static bifurcations. The applicable range of the modified Lindstedt－Poincaré method is extended to 1/2 subharmonic resonance systems. The bifurcation equation of a strongly nonlinear oscillator, which is transformed into a small parameter system, is determined by the multiple scales method. On the basis of the singularity theory, the transition set and the bifurcation diagram in various regions of the parameter plane are analysed.

Key words: strongly nonlinear oscillator, parameter excitation, bifurcation

中图分类号:  (Synchronization; coupled oscillators)

  • 05.45.Xt
84.30.Ng (Oscillators, pulse generators, and function generators)