Noise-induced phase slips, log-periodic oscillations, and the Gumbel distribution

Abstract

When two synchronised phase oscillators are perturbed by weak noise, they display occasional losses of synchrony, called phase slips. The slips can be characterised by their location in phase space and their duration. We show that when properly normalised, their location converges, in the vanishing noise limit, to the sum of an asymptotically geometric random variable and a Gumbel random variable. The duration also converges to a Gumbel variable with different parameters. We relate these results to recent works on the phenomenon of log-periodic oscillations and on links between transition path theory and extreme-value theory.

32 pages, 6 figures

References in corpus (5)

• On the noise-induced passage through an unstable periodic orbit II: General case
• Universality of residence-time distributions in non-adiabatic stochastic resonance
• Oscillatory critical amplitudes in hierarchical models and the tail of the Harris random variable
• Suppression of thermally activated escape by heating
• Gumbel distribution in exit problems