Synchronization of oscillators in a Kuramoto-type model with generic coupling

TL;DR

This paper investigates synchronization in a generalized Kuramoto model with diverse coupling contributions, providing explicit solutions for mean field properties and analyzing effects like finite signal velocity on spatially distributed oscillators.

Contribution

It introduces a generalized Kuramoto-type model with variable oscillator contributions and derives explicit self-consistency solutions for the mean field in both noise-free and noisy scenarios.

Findings

Explicit solutions for mean field amplitude and frequency

Analysis of spatially distributed oscillators with finite signal velocity

Generalization of Kuramoto model to include diverse coupling effects

Abstract

We study synchronization properties of coupled oscillators on networks that allow description in terms of global mean field coupling. These models generalize the standard Kuramoto-Sakaguchi model, allowing for different contributions of oscillators to the mean field and to different forces from the mean field on oscillators. We present the explicit solutions of self-consistency equations for the amplitude and frequency of the mean field in a parametric form, valid for noise-free and noise-driven oscillators. As an example we consider spatially spreaded oscillators, for which the coupling properties are determined by finite velocity of signal propagation.