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

作　　者：秦朝红 陈予恕 

机构地区：[1]The School of Astronautics, Harbin Institute of Technology [2]The School of Mechanical Engineering, Tianjin University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2010年第8期1019-1026,共8页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (No. 10632040)

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） λ 1 is considered as bifurcation parameter, （2） λ 2 is considered as bifurcation parameter, and （3） λ 1 and λ 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.Bifurcation properties of a Duffing-van der Pol system with two parameters under multi-frequency excitations are studied. Three cases are discussed： （1） λ 1 is considered as bifurcation parameter, （2） λ 2 is considered as bifurcation parameter, and （3） λ 1 and λ 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.

关 键 词：Duffing-van der Pol system two parameters singularity analysis 

分 类 号：O175.5[理学—数学]