Microscopic correlations in the finitesize Kuramoto model of coupled oscillators
Abstract
Supercritical Kuramoto oscillators with distributed frequencies can be separated into two disjoint groups: an ordered one locked to the mean field, and a disordered one consisting of effectively decoupled oscillators—at least so in the thermodynamic limit. In finite ensembles, in contrast, such clear separation fails: The mean field fluctuates due to finitesize effects and thereby induces order in the disordered group. This publication demonstrates this effect, similar to noiseinduced synchronization, in a purely deterministic system. We start by modeling the situation as a stationary mean field with additional white noise acting on a pair of unlocked Kuramoto oscillators. An analytical expression shows that the crosscorrelation between the two increases with decreasing ratio of natural frequency difference and noise intensity. In a deterministic finite Kuramoto model, the strength of the meanfield fluctuations is inextricably linked to the typical natural frequency difference. Therefore, we let a fluctuating mean field, generated by a finite ensemble of active oscillators, act on pairs of passive oscillators with a microscopic natural frequency difference between which we then measure the crosscorrelation, at both super and subcritical coupling.
 Publication:

Physical Review E
 Pub Date:
 September 2019
 DOI:
 10.1103/PhysRevE.100.032210
 arXiv:
 arXiv:1901.02779
 Bibcode:
 2019PhRvE.100c2210P
 Keywords:

 Nonlinear Sciences  Adaptation and SelfOrganizing Systems
 EPrint:
 7 pages