Analysis of a Nonlinear First-Order System with a White Noise Input

A general technique for computing the power spectrum of nonlinear systems is presented, and the method is applied to the Brownian motion of a particle with idealized Coulomb damping. In this method the transition probability is obtained by solving the appropriate Fokker-Planck equation. Then the autocorrelation function is calculated by an appropriate integration, and finally the power spectrum is found by means of the Wiener-Khintchine relation. Comparison is made with the method of equivalent linearization, which is applicable to a wide class of nonlinear problems