RESPONSE STATISTICS OF VANDERPOL OSCILLATORS EXCITED BY WHITE-NOISE

The joint probability density function of the state space vector of a white noise excited van der Pol oscillator satisfies a Fokker-Planck-K olmogorov (FPK) equation. The paper describes a numerical procedure fo r solving the transient FPK equation based on the path integral soluti on (PIS) technique. It is shown that by combining the PIS with a cubic B-spline interpolation method, numerical solution algorithms can be i mplemented giving solutions of the FPK equation that can be made accur ate down to very low probability levels. The method is illustrated by application to two specific examples of a van der Pol oscillator.