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

被引：5
|
作者：
Qin, Zhao-hong [1 ]
Chen, Yu-shu [1 ,2 ]
机构：
[1] Harbin Inst Technol, Sch Astronaut, Harbin 150001, Peoples R China
[2] Tianjin Univ, Sch Mech Engn, Tianjin 300072, Peoples R China
来源：
APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION | 2010年 / 31卷 / 08期
基金：
中国国家自然科学基金;
关键词：
Duffing-van der Pol system; two parameters; singularity analysis; HARMONIC OSCILLATOR; DYNAMICS;
D O I：
10.1007/s10483-010-1337-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
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) lambda (1) is considered as bifurcation parameter, (2) lambda (2) is considered as bifurcation parameter, and (3) lambda (1) and lambda (2) 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.
引用
收藏
页码：1019 / 1026
页数：8
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