Systematic adiabatic analysis of a nonlinear oscillator with inertia driven by colored noise

Abstract
The Duffing oscillator with inertia excited by colored noise is studied and a colored Fokker-Planck equation and reduced stationary probability density function is obtained by systematic adiabatic expansion. The second-order moments are presented for different values of system parameters and numerical simulation is carried out. In the region where perturbation is valid, i.e., where ε∼0.1, and when correlation time τ of noise is of the same order of system time scale 1/γ, the results of adiabatic expansion agree very well with that of numerical simulation.