One node driving synchronisation

TL;DR

This paper reveals that in complex networks of coupled phase-oscillators, a single key node can trigger global synchronization, with the critical node identified by a maximum ratio of natural frequency to coupling strength.

Contribution

It introduces a novel method to determine the critical coupling strength and identifies the key oscillator influencing network synchronization.

Findings

Synchronization is independent of natural frequency distribution.

A single oscillator can trigger network-wide synchronization.

The key oscillator is determined by the maximum ratio of natural frequency to coupling strength.

Abstract

Abrupt changes of behaviour in complex networks can be triggered by a single node. This work describes the dynamical fundamentals of how the behaviour of one node affects the whole network formed by coupled phase-oscillators with heterogeneous coupling strengths. The synchronisation of phase-oscillators is independent of the distribution of the natural frequencies, weakly depends on the network size, but highly depends on only one key oscillator whose ratio between its natural frequency in a rotating frame and its coupling strength is maximum. This result is based on a novel method to calculate the critical coupling strength with which the phase-oscillators emerge into frequency synchronisation. In addition, we put forward an analytical method to approximately calculate the phase-angles for the synchronous oscillators.