We study the effects of noise on the dynamics of a weakly damped van der Pol—Duffing oscillator. In the case of additive white noise, maxima in the stationary probability density correspond to stable stationary points of the unperturbed oscillator, and ridges correspond to stable limit cycles. Multiplicative white noise differs in the possibility of a noise-induced bifurcation for some parameter values. Our results are widely applicable because the oscillator we study also describes the dynamics near a common codimension-2 bifurcation.

• Received 28 April 1982

DOI:https://doi.org/10.1103/PhysRevA.26.2946