Modeling the Response of Rayleigh - Van der Pol Oscillators to Stochastic Excitation Near the Hopf Bifurcation

The Rayleigh-van der Pol equation for nonlinear oscillation has been a useful model for studying critical behavior near a Hopf bifurcation, including effects of external forcing and noise. Moreover, this equation has been found to be a good model of the long-term behavior of an experimental system consisting of the Wien bridge oscillator. We will describe work to study measures of noise variance, phase relations and other features of this combined model and experimental system, extended to coupling of two or more oscillators.