Stochastic averaging of quasi partially integrable Hamiltonian systems under fractional Gaussian noise

作     者：Qiang-feng LU Mao-lin DENG Wei-qiu ZHU 

作者机构：Department of Mechanics Zhefiang University Hangzhou 310077 China State Key Laboratory of Fluid Power and Mechatronic Systems Zhejiang University Hangzhou 310027 China Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province Zhejiang University Hangzhou 310027 China 

出 版 物：《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 (浙江大学学报（英文版）A辑（应用物理与工程）)

年 卷 期：2017年第18卷第9期

页      面：704-717页

核心收录：

学科分类：0810[工学-信息与通信工程] 04[教育学] 0805[工学-材料科学与工程（可授工学、理学学位）] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：supported by the National Natural Science Foundation of China(Nos.11172259 11272279 11321202 and 11432012) 

主　　题：Fractional Brownian motion (fBm) Fractional Gaussian noise (fGn) Quasi partially integrable Hamiltonian system Stochastic averaging method Stationary response 

摘      要：A stochastic averaging method for predicting the response of quasi partially integrable and non-resonant Hamiltoniansystems to fractional Gaussian noise （fGla） with the Hurst index 1/2〈H〈l is proposed. The averaged stochastic differential equa-tions （SDEs） for the first integrals of the associated Hamiltonian system are derived. The dimension of averaged SDEs is less thanthat of the original system. The stationary probability density and statistics of the original system are obtained approximately fromsolving the averaged SDEs numerically. Two systems are worked out to illustrate the proposed stochastic averaging method. It isshown that the results obtained by using the proposed stochastic averaging method and those from digital simulation of originalsystem agree well, and the computational time for the former results is less than that for the latter ones.