Stochastic response of fractional-order van der Pol oscillator

Abstract

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.

Keywords

• fractional-order van de Pol oscillator
• Gaussian white noise
• stationary response
• equivalent nonlinear system method
• stochastic averaging