Stochastic response of fractional-order van der Pol oscillator

Theoretical and Applied Mechanics Letters

Lincong Chen¹  Weiqiu Zhu² 

[1] College of Civil Engineering, Huaqiao University, Xiamen 361021, China;Department of Mechanics, Zhejiang University, Hangzhou 310027, China;

关键词: fractional-order van de Pol oscillator;    Gaussian white noise;    stationary response;    equivalent nonlinear system method;    stochastic averaging;   

DOI  :  10.1063/2.1401310

来源: DOAJ

【 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 Itô equation is deduced. We obtained the Fokker-Planck-Kolmogorov equation connected to the averaged Itô equation and solved it to yield the approximate stationary response of the system. The analytical solution is confirmed by using Monte Carlo simulation.

【 授权许可】

Unknown