ANALYTICAL STUDY OF THE DUFFING OSCILLATOR EXCITED BY COLORED NOISE USING A SYSTEMATIC ADIABATIC EXPANSION

Analytical studies of nonlinear systems driven by colored noise are qu ite involved. If the inertia of the system is included in analysis, th e results are physically realistic although the problem becomes more c omplex. Research along this line is in progress and this paper is an e ffort to study a nonlinear oscillator excited by correlated noise. The work delves on the Duffing oscillator driven by exponentially correla ted noise. The colored Fokker-Planck equation is derived and the metho d of systematic adiabatic expansion is used to obtain the reduced prob ability density function from which the second-order moments are evalu ated for different values of system parameters. Numerical simulation i s carried out by generating colored noise using the spectral method. i n the region where perturbation is valid, the results of adiabatic exp ansion agree very well with that of Monte Carlo simulation.