Stochastic bifurcation in duffing system subject to harmonic excitation and in presence of random noise

Wei Xu, Qun He, Tong Fang, Haiwu Rong

Research output: Contribution to journalArticlepeer-review

60 Scopus citations

Abstract

A global analysis of stochastic bifurcation in a special kind of Duffing system, named as Ueda system, subject to a harmonic excitation and in presence of random noise disturbance is studied in detail by the generalized cell mapping method using digraph. It is found that for this dissipative system there exists a steady state random cell flow restricted within a pipe-like manifold, the section of which forms one or two stable sets on the Poincare cell map. These stable sets are called stochastic attractors (stochastic nodes), each of which owns its attractive basin. Attractive basins are separated by a stochastic boundary, on which a stochastic saddle is located. Hence, in topological sense stochastic bifurcation can be defined as a sudden change in character of a stochastic attractor when the bifurcation parameter of the system passes through a critical value. Through numerical simulations the evolution of the Poincare cell maps of the random flow against the variation of noise intensity is explored systematically. Our study reveals that as a powerful tool for global analysis, the generalized cell mapping method using digraph is applicable not only to deterministic bifurcation, but also to stochastic bifurcation as well. By this global analysis the mechanism of development, occurrence, and evolution of stochastic bifurcation can be explored clearly and vividly.

Original languageEnglish
Pages (from-to)1473-1479
Number of pages7
JournalInternational Journal of Non-Linear Mechanics
Volume39
Issue number9
DOIs
StatePublished - Nov 2004

Keywords

  • Digraph
  • Duffing system
  • Global analysis
  • Stochastic attractor
  • Stochastic bifurcation
  • Stochastic saddle
  • The generalized cell mapping method

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