Remarks on stochastic resonance

Abstract

A recent and interesting experimental paper [B. McNamara, K. Wiesenfeld, and R. Roy, Phys. Rev. Lett. 60, 2626 (1988)] has refocused attention on the problem of stochastic resonance by presenting measurements of the singal-to-noise ratio (SNR) of a noise driven, periodically modulated bistable ring laser. We point out that the theoretical SNR, as defined in this and a previous work, is always infinity, because additive modulation leads to a \ensuremath{\delta} function in the power spectrum of the output. Quantitative information on stochastic resonance is contained in the strength of this \ensuremath{\delta} function relative to the noise background. We qualitatively reproduce the SNR data with an analog simulator using a standard quartic bistable potential. In this, as in previous experiments and simulations, a peak in the observed power spectrum is a reflection of the \ensuremath{\delta} function, but the amplitude of the peak is rendered finite (and hence measureable) only because of the finite resolution of the measurement system.