Power Spectra of Systems Described by a Nonlinear Langevin Equation Driven by Random and Periodic Forces

Abstract

Simulation was performed both by a digital computer and by an analog circuit connected to a micro-computer, and stationary power spectra were measured. When only Gaussian white noise force was applied additively to an equation of inactive type, was observed the Lorentzian power spectrum, whose density decreased with increasing nonlinearity in low frequency region. An equation of active type also exhibits the Lorentzian power spectrum if random force was week. When random and periodic forces were applied simultaneously, the continuous part of the power spectrum was also Lorentzian, but the low frequency density was reduced considerably. The experimentally obtained results were consistent with those obtained theoretically by using the statistical linearization approximation developed by Budger, Lindenberg and Shuler.