Noise-induced chaotic motions in Hamiltonian systems with slow-varying parameters |
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Authors: | Wang Shuanglian Guo Yimu Gan Chunbiao |
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Institution: | (1) Department of Mechanics, Zhejiang University, 310027 Hangzhou, China |
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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. |
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Keywords: | Hamiltonian system slow-varying parameter Gaussian white noise stochastic melnikov method chaotic motion |
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