A Chakraborty

A Politi

AS Pikovsky

C Freitas

D Aeyels

DJ Watts

E Niebur

G Filatrella

H Hong

H Kori

I Leyva

J Teramae

JA Rogge

JC Bronski

L Glass

M Verwoerd

MG Rosenblum

MJ Lee

OV Popovych

PC Matthews

PH Nardelli

R Carareto

SH Strogatz

VN Belykh

W Yu

Y Kuramoto

Y Tang

Z Zheng

Scientific Reports

AbstractAbrupt 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.</jats:p

One node driving synchronisation

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