Noise-induced phase locking in a relaxation oscillator: a Kramers rate characterization

It has been shown that phase locking in a Wiener (“integrate-and-fire”) process can be improved by additive noise. Relaxation oscillators, and other electronic systems that display limit cycling, can be modeled as Wiener processes; it has been suggested that they will display stochastic resonance and other types of co-operative behavior, particularly in the presence of colored noise. We demonstrate stochastic phase locking in a simple relaxation oscillator, and show that the ratio of input frequency to output frequency can be selected according to the variance of the additive noise. By performing a prior Kramers rate characterization, the optimal level of noise can be applied in advance if the input frequency is known to some approximate value