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

Nils Berglund
Markov Processes Relat. Fields 22:467-505 (2016)

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.

Mathematical Subject Classification: 60H10, 34F05 (primary), 60G70, 34D06 (secondary).

Keywords and phrases: Synchronization, phase slip, stochastic exit problem, large deviations, random Poincaré map, log-periodic oscillations, cycling, transition-path theory, extreme-value theory, Gumbel distribution.

 

Journal Homepage Published article MR3585827 Zbl1356.60089

PDF file (687 Kb) hal-00967427 arXiv/1403.7393