Stochastic averaging of quasi partially integrable Hamiltonian systems under fractional Gaussian noise |
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Authors: | " target="_blank">Qiang-feng Lü Mao-lin Deng Wei-qiu Zhu |
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Institution: | 1.Department of Mechanics,Zhejiang University,Hangzhou,China;2.State Key Laboratory of Fluid Power and Mechatronic Systems,Zhejiang University,Hangzhou,China;3.Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province,Zhejiang University,Hangzhou,China |
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Abstract: | A stochastic averaging method for predicting the response of quasi partially integrable and non-resonant Hamiltonian systems to fractional Gaussian noise (fGn) with the Hurst index 1/2<H<1 is proposed. The averaged stochastic differential equations (SDEs) for the first integrals of the associated Hamiltonian system are derived. The dimension of averaged SDEs is less than that of the original system. The stationary probability density and statistics of the original system are obtained approximately from solving the averaged SDEs numerically. Two systems are worked out to illustrate the proposed stochastic averaging method. It is shown that the results obtained by using the proposed stochastic averaging method and those from digital simulation of original system agree well, and the computational time for the former results is less than that for the latter ones. |
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