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Applied Mathematics and Mechanics (English Edition) ›› 2010, Vol. 31 ›› Issue (8): 1019-1026.doi: https://doi.org/10.1007/s10483-010-1337-7

• Articles • 上一篇    下一篇

Singularity analysis of Duffing-van der Pol system with two bifurcation parameters under multi-frequency excitations

秦朝红1 陈予恕1,2   

  1. 1. The School of Astronautics, Harbin Institute of Technology, Harbin 150001, P. R. China;
    2. The School of Mechanical Engineering, Tianjin University, Tianjin 300072, P. R. China
  • 收稿日期:2010-02-26 修回日期:2010-05-29 出版日期:2010-07-23 发布日期:2010-08-01

Singularity analysis of Duffing-van der Pol system with two bifurcation parameters under multi-frequency excitations

 QIN Zhao-Hong1, CHEN Yu-Shu1,2   

  1. 1. The School of Astronautics, Harbin Institute of Technology, Harbin 150001, P. R. China;
    2. The School of Mechanical Engineering, Tianjin University, Tianjin 300072, P. R. China
  • Received:2010-02-26 Revised:2010-05-29 Online:2010-07-23 Published:2010-08-01

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被引次数

12

摘要： Bifurcation properties of a Duffing-van der Pol system with two parameters under multi-frequency excitations are studied. Three cases are discussed: (1) λ1 is considered as bifurcation parameter, (2) λ2 is considered as bifurcation parameter, and (3) λ1 and λ2 are both considered as bifurcation parameters. According to the definition of transition sets, the whole parametric space is divided into several different persistent regions by the transition sets for different cases. The bifurcation diagrams in different persistent regions are obtained, which provides a theoretical basis for optimal design of the system.

Abstract: Bifurcation properties of a Duffing-van der Pol system with two parameters under multi-frequency excitations are studied. Three cases are discussed: (1) λ1 is considered as bifurcation parameter, (2) λ2 is considered as bifurcation parameter, and (3) λ1 and λ2 are both considered as bifurcation parameters. According to the definition of transition sets, the whole parametric space is divided into several different persistent regions by the transition sets for different cases. The bifurcation diagrams in different persistent regions are obtained, which provides a theoretical basis for optimal design of the system.

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