Analytical Study of the Duffing Oscillator Excited by Colored Noise Using a Systematic Adiabatic Expansion

Abstract

Analytical studies of nonlinear systems driven by colored noise are quite involved. If the inertia of the system is included in analysis, the results are physically realistic although the problem becomes more complex. Research along this line is in progress and this paper is an effort to study a nonlinear oscillator excited by correlated noise. The work delves on the Duffing oscillator driven by exponentially correlated noise. The colored Fokker-Planck equation is derived and the method of systematic adiabatic expansion is used to obtain the reduced probability density function from which the second-order moments are evaluated for different values of system parameters. Numerical simulation is carried out by generating colored noise using the spectral method. In the region where perturbation is valid, the results of adiabatic expansion agree very well with that of Monte Carlo simulation.