FREQUENCY FLUCTUATIONS IN NOISY OSCILLATORS.

We study frequency and period fluctuations in a nonlinear oscillator driven by Gaussian white noise. We define the random period as the random time between two consecutive zero crossings by the random phase plane trajectory, and the random frequency as the number of such zero crossings per unit of time. These quantities are shown to be related by renewal theory. We find asymptotic expressions for the means of variances of the random period and random frequency, for small damping and small noise. The formulas are particularly useful for oscillators with high frequency.