Approximate solution for frequency synchronisation in a finite-size Kuramoto model
Abstract
Scientists have been considering the Kuramoto model to understand the mechanism behind the appearance of collective behaviour, such as frequency synchronisation (FS) as a paradigm, in real-world networks with a finite number of oscillators. A major current challenge is to obtain an analytical solution for the phase-angles. Here, we provide an approximate analytical solution for this problem by deriving a master solution for the finite-size Kuramoto model, without imposing any restriction on the distribution of the natural frequencies of the oscillators. The master solution embodies all particular solutions of the finite-size Kuramoto model for any frequency distribution and coupling strength larger than the critical one. Furthermore, we present a criterion to determine the stability of the FS solution. This allows one to analytically infer the relationship between the physical parameters and the stable behaviour of networks.
Keywords
Cite
@article{arxiv.1509.04244,
title = {Approximate solution for frequency synchronisation in a finite-size Kuramoto model},
author = {Chengwei Wang and Nicolas Rubido and Celso Grebogi and Murilo S. Baptista},
journal= {arXiv preprint arXiv:1509.04244},
year = {2015}
}