Advertisement

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
Article
  • 33 Downloads

Abstract

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 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Kevorkian J, Cole JD. Perturbation Methods in Applied Mechanics. New York: Springer-Verlag, 1981Google Scholar
  2. 2.
    Allen JS, Samelson RM, Newberger PA. Chaos in a model of forced quasi-geostrophic flow over topography: An application of Melnikov's method.J Fluid Mech, 1991, 226: 511–547MATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    Thompson JMT, Rainey RCT, Soliman MS. Ship stability criteria based on chaotic transients from incursive fractals.Philosophical Trans of the Royal Soc of London A, 1990, 332: 149–167MATHMathSciNetGoogle Scholar
  4. 4.
    Yim SCS, Lin H. Probabilistic analysis of a chaotic dynamical system. In: Applied Chaos, Kim JH and Stinger J (Eds), New York: Wiley, 1992Google Scholar
  5. 5.
    Frey M, Simiu E. Noise-induced chaos and phase space flux.Physica D, 1993, 63: 321–340MATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Xie WM. Effect of noise on chaotic motion of buckled column under periodic excitation.ASME Nonlinear and Stochastic Dynamics, 1994, AMD-Vol 192/DE-Vol 73: 215–225Google Scholar
  7. 7.
    Lin H, Yim SCS. Analysis of a nonlinear systems exhibiting chaotic, noisy chaotic and random behaviors.ASME Journal of Applied Mechanics, 1996, 63: 509–516MATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    Wiggins S. Global Bifurcations and Chaos, New York: Springer-Verlag, 1990MATHGoogle Scholar
  9. 9.
    Gan CB, Guo YM. Noise-induced chaotic motions in quasi-integrable Hamiltonian systems.Acta Mech Sinica, 2000, 32(5): 613–620 (in Chinese)Google Scholar
  10. 10.
    Zhu WQ. Stochastic Oscillations. Beijing: Science Press, 1998 (in Chinese)Google Scholar

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

Personalised recommendations