Stochastic phase portraits of a damped bistable oscillator driven by colored noise

Abstract

We present measurements of the stationary, joint statistical densities of velocity and displacement in a three-dimensional system: the damped oscillator with a bistable potential driven by additive, colored noise. Approximate Fokker-Planck theories of such "higher-dimensional" systems are assessed and compared to the measurements. Because of limitations inherent in all present theories and generally available numerical techniques, analog simulators appear to offer the only effective, high-resolution means for obtaining the joint probability densities of $d=3\mathrm{}$ systems.