A minimal model of partial synchrony
Adaptation and Self-Organizing Systems
2017-06-02 v1
Abstract
We show that self-consistent partial synchrony in globally coupled oscillatory ensembles is a general phenomenon. We analyze in detail appearance and stability properties of this state in possibly the simplest setup of a biharmonic Kuramoto-Daido phase model as well as demonstrate the effect in limit-cycle relaxational Rayleigh oscillators. Such a regime extends the notion of splay state from a uniform to distribution of phases to an oscillating one. Suitable collective observables such as the Kuramoto order parameter allow detecting the presence of a inhomogeneous distribution. The characteristic and most peculiar property of partial synchrony is the difference between the frequencies of single units and that of the macroscopic field.
Cite
@article{arxiv.1607.07178,
title = {A minimal model of partial synchrony},
author = {Pau Clusella Cobero and Antonio Politi and Michael Rosenblum},
journal= {arXiv preprint arXiv:1607.07178},
year = {2017}
}