Noise tolerance of frequency-locked dynamics

We study the effect of noise on systems having two competing frequencies. In a mode-locked state, random perturbations are effectively suppressed, while outside a locking interval relatively high levels of broadband noise are observed, a correspondence first noted in experiments on charge-density waves. This correspondence is a general phenomenon and can be understood by simple dynamical considerations, as illustrated by the noisy circle map. We compare our analytic results for the observed power spectrum with digital simulations, and suggest tests of the theory for future experiments.