Acta Mechanica Sinica

, Volume 17, Issue 3, pp 281–288 | Cite as

Noise-induced chaotic motions in Hamiltonian systems with slow-varying parameters

  • Wang Shuanglian
  • Guo Yimu
  • Gan Chunbiao


This paper studies chaotic motions in quasi-integrable Hamiltonian systems with slow-varying parameters under both harmonic and noise excitations. Based on the dynamic theory and some assumptions of excited noises, an extended form of the stochastic Melnikov method is presented. Using this extended method, the homoclinic bifurcations and chaotic behavior of a nonlinear Hamiltonian system with weak feed-back control under both harmonic and Gaussian white noise excitations are analyzed in detail. It is shown that the addition of stochastic excitations can make the parameter threshold value for the occurrence of chaotic motions vary in a wider region. Therefore, chaotic motions may arise easily in the system. By the Monte-Carlo method, the numerical results for the time-history and the maximum Lyapunov exponents of an example system are finally given to illustrate that the presented method is effective.

Key Words

Hamiltonian system slow-varying parameter Gaussian white noise stochastic melnikov method chaotic motion 


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Copyright information

© Chinese Society of Theoretical and Applied Mechanics 2001

Authors and Affiliations

  • Wang Shuanglian
    • 1
  • Guo Yimu
    • 1
  • Gan Chunbiao
    • 1
  1. 1.Department of MechanicsZhejiang UniversityHangzhouChina

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