Open AccessGlobal analysis of stochastic bifurcation in a Duffing-van der Pol system
Author(s) -
Wei Xu,
Qun He,
Rong Hai-Wu,
Tong Fang
Publication year - 2003
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.52.1365
Subject(s) - saddle node bifurcation , bifurcation , bifurcation diagram , digraph , attractor , biological applications of bifurcation theory , mathematics , van der pol oscillator , bifurcation theory , infinite period bifurcation , stochastic process , pitchfork bifurcation , homoclinic bifurcation , statistical physics , mathematical analysis , nonlinear system , physics , discrete mathematics , statistics , quantum mechanics
Stochastic bifurcation of the Duffing-van der Pol oscillators under both additive and multiplicative random excitations is studied in detail by the generalized cell mapping method using digraph.As an alternative definition,stochastic bifurcation may be defined as a sudden change in character of a stochastic attractor when the bifurcation parameter of the system passes through a critical value.It is found that under certain conditions stochastic bifurcation mostly occurs when a stochastic attractor collides with a stochastic saddle.Our study reveals that the generalized cell mapping method with digraph is also a powerful tool for global analysis of stochastic bifurcation.By this global analysis ,the mechanism of development,occurrence,and evolution of a stochastic bifurcation can be explored clearly and vividly.