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

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  • 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 date: 2010-02-26

  Revised date: 2010-05-29

  Online published: 2010-08-01

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.

Cite this article

QIN Zhao-Hong;CHEN Yu-Shu . Singularity analysis of Duffing-van der Pol system with two bifurcation parameters under multi-frequency excitations[J]. Applied Mathematics and Mechanics, 2010 , 31(8) : 1019 -1026 . DOI: 10.1007/s10483-010-1337-7

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