Stochastic response of fractional-order van der Pol oscillator  

作　　者：Lincong Chen Weiqiu Zhu 

机构地区：[1]College of Civil Engineering, Huaqiao University [2]Department of Mechanics, Zhejiang University

出　　处：《Theoretical & Applied Mechanics Letters》2014年第1期68-72,共5页力学快报（英文版）

基　　金：supported by the National Natural Science Foundation of China(10932009,11072212,11272279,and 11002059);the Specialized Research Fund for the Doctoral Program of Higher Education(20103501120003);the Fundamental Research Funds for Huaqiao University(JB-SJ1010)

摘　　要：We studied the response of fractional-order van de Pol oscillator to Gaussian white noise excitation in this letter. An equivalent integral-order nonlinear stochastic system is obtained to replace the given system based on the principle of minimum mean-square error. Through stochastic averaging, an averaged Ito equation is deduced. We obtained the Fokker–Planck–Kolmogorov equation connected to the averaged Ito equation and solved it to yield the approximate stationary response of the system. The analytical solution is confirmed by using Monte Carlo simulation.We studied the response of fractional-order van de Pol oscillator to Gaussian white noise excitation in this letter. An equivalent integral-order nonlinear stochastic system is obtained to replace the given system based on the principle of minimum mean-square error. Through stochastic averaging, an averaged Ito equation is deduced. We obtained the Fokker–Planck–Kolmogorov equation connected to the averaged Ito equation and solved it to yield the approximate stationary response of the system. The analytical solution is confirmed by using Monte Carlo simulation.

关 键 词：fractional-order van de Pol oscillator Gaussian white noise stationary response equivalent nonlinear system method stochastic averaging 

分 类 号：O211.6[理学—概率论与数理统计]