Acta Mechanica Solida Sinica

, Volume 30, Issue 1, pp 11–19 | Cite as

Stochastic averaging of quasi integrable and resonant Hamiltonian systems excited by fractional Gaussian noise with Hurst index 1/2 <H < 1

  • Q. F. Lü
  • M. L. Deng
  • W. Q. Zhu


A stochastic averaging method of quasi integrable and resonant Hamiltonian systems under excitation of fractional Gaussian noise (fGn) with the Hurst index 1/2 < H < 1 is proposed. First, the definition and the basic property of fGn and related fractional Brownian motion (fBm) are briefly introduced. Then, the averaged fractional stochastic differential equations (SDEs) for the first integrals and combinations of angle variables of the associated Hamiltonian systems are derived. The stationary probability density and statistics of the original systems are then obtained approximately by simulating the averaged SDEs numerically. An example is 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.


Quasi integrable and resonant Hamiltonian system Fractional Brownian motion Fractional Gaussian noise Stochastic averaging method Internal resonant 


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2014

Authors and Affiliations

  1. 1.Department of Mechanics, State Key Laboratory of Fluid Power and Mechatronic Systems, Key Laboratory of Soft Machines and Smart Devices of Zhejiang ProvinceZhejiang UniversityHangzhouChina

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