Response of Quasi-Integrable and Non-Resonant Hamiltonian Systems to Fractional Gaussian Noise

Abstract

The main difficulty of analyzing the response of nonlinear dynamical systems to fractional Gaussian noise (fGn) is the non-Markov property and non-usefulness of diffusion process theory. Currently, only numerical simulation can be applied to obtain the response of nonlinear systems to fGn. In the present paper, noting the rather flat property of the fGn power spectral density (PSD) in most part of frequency band, the stochastic averaging method for quasi-integrable Hamiltonian systems under wide-band noise excitation is applied to predict the response of quasi-integrable and non-resonant Hamiltonian systems to fGn. By using this method, the averaged Itô stochastic differential equations (SDEs) are established and the probability density function (PDF) of system response can be obtained from solving the corresponding Fokker-Planck-Kolmogorov (FPK) equation. All of the statistics of system response are then obtained from the PDF analytically and verified through the comparison with the simulation results.

Keywords

• Fractional Gaussian noise
• quasi-integrable and non-resonant Hamiltonian systems
• stochastic averaging method