Open AccessBifurcation analysis of a compound oscillator with parametric and external excitation
Author(s) -
Ji Ying,
Qinsheng Bi
Publication year - 2009
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.58.4431
Subject(s) - homoclinic bifurcation , biological applications of bifurcation theory , bifurcation , heteroclinic bifurcation , transcritical bifurcation , saddle node bifurcation , parametric statistics , pitchfork bifurcation , excitation , bifurcation diagram , nonlinear system , bifurcation theory , bogdanov–takens bifurcation , period doubling bifurcation , homoclinic orbit , hopf bifurcation , physics , mathematical analysis , statistical physics , mathematics , quantum mechanics , statistics
The dynamics of a compound oscillator with parametric and external excitation has been investigated. Local bifurcation analysis of the first order approximation shows that simple bifurcation as well as Hopf bifurcation may take placeas have been observed in the original system. The influence of several parameters on the dynamics has been exploredwhich reveals that different nonlinear behaviors can be obtained with the variation of the parameters. Furthermoreby employing global bifurcation theorythe necessary conditions for homoclinic and heteroclinic bifurcation has been presentedwhich agrees well with the numerical results.