Random oscillation in systems subject to the excitation of a class of coloured noises

Abstract

In the paper the higher order stochastic averaging method is developed to a class of colored noise excitations when the corresponding forming filter has only finite negative eigenvalues. The second approximate probability density function to the Duffing system subject to the exponentially correlated process is obtained. Numerical application is carried out to investigate the independence of mean square amp1itude on the bandwidth parameter.