  The effect of small-amplitude noise on excitable systems with large
time-scale separation is analyzed. It is found that small random perturbations
of the fast excitatory variable result in the onset of a quasi-deterministic
limit cycle behavior, absent without noise. The limit cycle is established at a
critical value of the amplitude of the noise, and its period is nontrivially
determined by the relationship between the noise amplitude and the time scale
ratio. It is argued that this effect might provide a mechanism by which the
function of biological systems operating in noisy environments can be robustly
controlled by the level of the noise.
