Nonlinear Dynamics

, Volume 42, Issue 2, pp 185–198 | Cite as

Bifurcation and Chaos Analysis of Stochastic Duffing System Under Harmonic Excitations

  • X. L. Leng
  • C. L. Wu
  • X. P. Ma
  • G. Meng
  • T. Fang
Article
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Accepted:

Abstract

The Chebyshev polynomial approximation is applied to the dynamic response problem of a stochastic Duffing system with bounded random parameters, subject to harmonic excitations. The stochastic Duffing system is first reduced into an equivalent deterministic non-linear one for substitution. Then basic non-linear phenomena, such as stochastic saddle-node bifurcation, stochastic symmetry-breaking bifurcation, stochastic period-doubling bifurcation, coexistence of different kinds of steady-state stochastic responses, and stochastic chaos, are studied by numerical simulations. The main feature of stochastic chaos is explored. The suggested method provides a new approach to stochastic dynamic response problems of some dissipative stochastic systems with polynomial non-linearity.

Keywords

Chebyshev polynomial approximation stochastic bifurcation stochastic chaos stochastic Duffing system 
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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  • X. L. Leng
    • 1
  • C. L. Wu
    • 2
    • 3
  • X. P. Ma
    • 4
  • G. Meng
    • 1
  • T. Fang
    • 2
  1. 1.State Key Laboratory of Vibration, Shock, and Noise, School of Mechanical and Power Energy EngineeringShanghai Jiaotong UniversityShanghaiChina
  2. 2.Department of Engineering MechanicsNorthwestern Polytechnical UniversityXianChina
  3. 3.Aircraft Strength Research Institute of ChinaXianChina
  4. 4.Institute of UAVNorthwestern Polytechnical UniversityXian

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