Pseudo-regular oscillations induced by external noise

Abstract

An examination of the effect of noise on a general system at a saddle-node bifurcation has revealed that, in the limit of weak noise, the probability density of the time to pass through the saddle-node has a universal shape, the specific kinetics of the particular system serving only to set the time scale. This probability density is displayed and its salient features are explicated. In the case of a saddle-node bifurcation leading to relaxation oscillations, this analysis leads to the prediction of the existence of noise-induced oscillations which appear much less random than might at first be expected. The period of these oscillations has a well-defined, nonzero most probable value, the inverse of which is a noise-induced frequency. This frequency can be detected as a peak in power spectra from numerical simulations of such a system. This is the first case of the prediction and detection of a noise-induced frequency of which the authors are aware.