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

作     者：Q.F.Lü M.L.Deng W.Q.Zhu 

作者机构：Department of MechanicsState Key Laboratory of Fluid Power and Mechatronic SystemsKey Laboratory of Soft Machines and Smart Devices of Zhejiang ProvinceZhejiang University 

出 版 物：《Acta Mechanica Solida Sinica》 (固体力学学报（英文版）)

年 卷 期：2017年第30卷第1期

页      面：11-19页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 0805[工学-材料科学与工程（可授工学、理学学位）] 0802[工学-机械工程] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 0702[理学-物理学] 

基　　金：supported by the National Natural Science Foundation of China under grants nos.:11272279 11321202 and 11432012 

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

摘      要：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 （iBm） 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.