Analysis of stochastic bifurcation and chaos in stochastic Duffing-van der Pol system via Chebyshev polynomial approximation

Shao Juan Ma, Wei Xu, Wei Li, Tong Fang

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27 Scopus citations

Abstract

The Chebyshev polynomial approximation is applied to investigate the stochastic period-doubling bifurcation and chaos problems of a stochastic Duffing-van der Pol system with bounded random parameter of exponential probability density function subjected to a harmonic excitation. Firstly the stochastic system is reduced into its equivalent deterministic one and then the responses of stochastic system can be obtained by numerical methods. Nonlinear dynamical behaviour related to stochastic period-doubling bifurcation and chaos in the stochastic system is explored. Numerical simulations show that similar to its counterpart in deterministic nonlinear system of stochastic period-doubling bifurcation and chaos may occur in the stochastic Duffing-van der Pol system even for weak intensity of random parameter. Simply increasing the intensity of the random parameter may result in the period-doubling bifurcation which is absent from the deterministic system.

Original languageEnglish
Article number017
Pages (from-to)1231-1238
Number of pages8
JournalChinese Physics
Volume15
Issue number6
DOIs
StatePublished - 1 Jun 2006

Keywords

  • Chebyshev polynomial approximation
  • Stochastic chaos
  • Stochastic Duffing-van der Pol system
  • Stochastic period-doubling bifurcaton

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