Open AccessStochastic bifurcations in Duffing-van der Pol oscillator with Lévy stable noise
Author(s) -
Rencai Gu,
Yong Xu,
Mu Hao,
Zhiqiang Yang
Publication year - 2011
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.60.060513
Subject(s) - van der pol oscillator , probability density function , bistability , statistical physics , stationary distribution , noise (video) , physics , duffing equation , bifurcation , stability (learning theory) , mathematics , nonlinear system , quantum mechanics , computer science , statistics , artificial intelligence , machine learning , markov chain , image (mathematics)
This paper aims to investigate the influence of Lévy stable noise on a bistable Duffing-van der Pol oscillator. We obtain the stationary probability density function of amplitude for the Duffing-van der Pol oscillator by use of Monte Carlo method, and analyze the influences of the noise intensity and the stability index on the stationary probability density. Stochastic bifurcations are further discussed though a qualitative change of the stationary probability distribution, which indicates that not only system parameters and noise intensity can be treated as bifurcation parameters, but also the change of the stability index will induce stochastic bifurcations.