Stochastic response of van der Pol oscillator with two kinds of fractional derivatives under Gaussian white noise excitation  

作　　者：杨勇歌 徐伟 孙亚辉 谷旭东 

机构地区：[1]Department of Applied Mathematics, Northwestern Polytechnical University [2]State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi'an Jiaotong University [3]Department of Engineering Mechanics, Northwestern Polytechnical University

出　　处：《Chinese Physics B》2016年第2期13-21,共9页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Grant Nos.11472212,11532011,and 11502201)

摘　　要：This paper aims to investigate the stochastic response of the van der Pol （VDP） oscillator with two kinds of fractional derivatives under Gaussian white noise excitation. First, the fractional VDP oscillator is replaced by an equivalent VDP oscillator without fractional derivative terms by using the generalized harmonic balance technique. Then, the stochastic averaging method is applied to the equivalent VDP oscillator to obtain the analytical solution. Finally, the analytical solutions are validated by numerical results from the Monte Carlo simulation of the original fractional VDP oscillator. The numerical results not only demonstrate the accuracy of the proposed approach but also show that the fractional order, the fractional coefficient and the intensity of Gaussian white noise play important roles in the responses of the fractional VDP oscillator. An interesting phenomenon we found is that the effects of the fractional order of two kinds of fractional derivative items on the fractional stochastic systems are totally contrary.This paper aims to investigate the stochastic response of the van der Pol （VDP） oscillator with two kinds of fractional derivatives under Gaussian white noise excitation. First, the fractional VDP oscillator is replaced by an equivalent VDP oscillator without fractional derivative terms by using the generalized harmonic balance technique. Then, the stochastic averaging method is applied to the equivalent VDP oscillator to obtain the analytical solution. Finally, the analytical solutions are validated by numerical results from the Monte Carlo simulation of the original fractional VDP oscillator. The numerical results not only demonstrate the accuracy of the proposed approach but also show that the fractional order, the fractional coefficient and the intensity of Gaussian white noise play important roles in the responses of the fractional VDP oscillator. An interesting phenomenon we found is that the effects of the fractional order of two kinds of fractional derivative items on the fractional stochastic systems are totally contrary.

关 键 词：stochastic averaging method fractional derivative van der Pol equivalent stochastic system 

分 类 号：TN752[电子电信—电路与系统] O172[理学—数学]