Super-harmonic Resonance and Bifurcation of Duffing-van Der Pol System with Multi-Frequency Excitation

被引：0

作者：

Zhao, Wei-Guo ^{[1
]}

Wei, De-Hua ^{[2
]}

机构：

[1] Hebei Univ Engn, Ctr Educ Technol, Handan 056038, Peoples R China

[2] Hebei Univ Engn, Coll Water Conservancy & Hydropower, Handan 056021, Peoples R China

来源：

APPLIED MATHEMATICS & INFORMATION SCIENCES | 2013年 / 7卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Duper-Harmonic resonance; bifurcation; Duffing-Van der pol system; multi-frequency excitation;

D O I：

10.12785/amis/072L16

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper the super-harmonic resonance of duffing-van der pol system is investigated, and the multi-scale method is used to obtain the steady solutionthen the effects of all the parameters of the system on the amplitude-frequency curve are also discussed. Finally, the numerical method is used to verify the accordance. The simulation results show amplitude-frequency curve has the characteristic of pitchfork bifurcation in the turning point and all the bifurcation characteristics are obtained using the singularity theory. The results cannot only be used to analysize the periodic solutions of similar systems, but can play a good role for the involved nonlinear control.

引用

页码：487 / 491

页数：5

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