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 bas...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.展开更多
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)
文摘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.
