Open AccessPeriod-doubling bifurcation analysis of stochastic van der Pol system via Chebyshev polynomial approximation
Author(s) -
Shuping Ma,
Wei Xu,
Wei Li,
Jin Yan-Fei
Publication year - 2005
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.54.3508
Subject(s) - chebyshev polynomials , period doubling bifurcation , chebyshev filter , bifurcation , mathematics , van der pol oscillator , nonlinear system , chebyshev nodes , polynomial , mathematical analysis , physics , quantum mechanics
Chebyshev polynomial approximation is applied to the period-doubling bifurcation problem of a stochastic van der Pol system with bounded random parameters and subjected to harmonic excitations. Firstly, the stochastic system is reduced to its equivalent deterministic one, through which the response of the stochastic s ystem can be obtained by numerical methods. Nonlinear dynamical behavior related to various forms of stochastic period-doubling bifurcation in the stochastic sy stem is explored. Numerical simulations show that similar to their counterpart i n deterministic nonlinear system, various forms of period-doubling bifurcation m ay occur in the stochastic van der Pol system, but with some modified features. Numerical results also show that Chebyshev polynomial approximation can provide an effective approach to dynamical problems in stochastic nonlinear systems.