Kuramoto model, phase synchronisation and the network's core

TL;DR

This paper demonstrates a method to identify core nodes in a network based on their role in phase synchronization within the Kuramoto model, linking network structure to dynamic behavior.

Contribution

It introduces a way to determine core nodes in a network by analyzing phase synchronization in the Kuramoto model, connecting network topology with dynamic core identification.

Findings

Core nodes can be identified through their influence on phase synchronization.

The method links network structure to dynamic core formation.

Potential applications in understanding synchronization phenomena.

Abstract

In this note we show that for the Kuramoto model defined in a simple undirected graph it is possible to decide which nodes form the core of the network. The set of core-nodes is defined by its relevance to the phase synchronisation process.