CLC number: O32
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
Crosschecked: 2017-08-15
Cited: 0
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Qiang-feng Lü, Mao-lin Deng, Wei-qiu Zhu. Stochastic averaging of quasi partially integrable Hamiltonian systems under fractional Gaussian noise[J]. Journal of Zhejiang University Science A, 2017, 18(9): 704-717.
@article{title="Stochastic averaging of quasi partially integrable Hamiltonian systems under fractional Gaussian noise",
author="Qiang-feng Lü, Mao-lin Deng, Wei-qiu Zhu",
journal="Journal of Zhejiang University Science A",
volume="18",
number="9",
pages="704-717",
year="2017",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A1600541"
}
%0 Journal Article
%T Stochastic averaging of quasi partially integrable Hamiltonian systems under fractional Gaussian noise
%A Qiang-feng Lü
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%A Wei-qiu Zhu
%J Journal of Zhejiang University SCIENCE A
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%N 9
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%D 2017
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A1600541
TY - JOUR
T1 - Stochastic averaging of quasi partially integrable Hamiltonian systems under fractional Gaussian noise
A1 - Qiang-feng Lü
A1 - Mao-lin Deng
A1 - Wei-qiu Zhu
J0 - Journal of Zhejiang University Science A
VL - 18
IS - 9
SP - 704
EP - 717
%@ 1673-565X
Y1 - 2017
PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.A1600541
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.
The traditional stochastic averaging method of quasi Hamiltonian system is based on the theory of diffusion process. An important property of diffusion process is the Markov property. For a long time, many researchers are wondering what the stochastic averaging method would be like if the system response processes is not Markov process. The fractional Brownian motion is known as a non-Markov process. And it is also known that the system response process have to be non-Markov process when the system is excited by fractional Gaussian noise. I value the subject discussed in this manuscript. It is the first time that the stochastic averaging method of quasi Hamiltonian system is developed to the case of non-Markov process.
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