A minimal model of partial synchrony

TL;DR

This paper demonstrates that self-consistent partial synchrony is a widespread phenomenon in globally coupled oscillators, extending the concept of splay states to oscillating regimes and analyzing its stability and detection methods.

Contribution

It introduces a minimal biharmonic Kuramoto-Daido model to analyze partial synchrony and demonstrates its occurrence in Rayleigh oscillators, expanding understanding of collective oscillatory states.

Findings

Partial synchrony is a general and stable phenomenon.

The model extends splay states to oscillating regimes.

Order parameters can detect partial synchrony.

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.