The Kuramoto model in complex networks

FA Rodrigues, TKDM Peron, P Ji, J Kurths - Physics Reports, 2016‏ - Elsevier
Synchronization of an ensemble of oscillators is an emergent phenomenon present in
several complex systems, ranging from social and physical to biological and technological …

Critical phenomena in complex networks

SN Dorogovtsev, AV Goltsev, JFF Mendes - Reviews of Modern Physics, 2008‏ - APS
The combination of the compactness of networks, featuring small diameters, and their
complex architectures results in a variety of critical effects dramatically different from those in …

Ralph Kenna's scaling relations in critical phenomena

L Moueddene, A Donoso, B Berche - Entropy, 2024‏ - mdpi.com
In this note, we revisit the scaling relations among “hatted critical exponents”, which were
first derived by Ralph Kenna, Des Johnston, and Wolfhard Janke, and we propose an …

Finite-size effect in Kuramoto oscillators with higher-order interactions

A Suman, S Jalan - Chaos: An Interdisciplinary Journal of Nonlinear …, 2024‏ - pubs.aip.org
Finite-size systems of a Kuramoto model display intricate dynamics, especially in the
presence of multi-stability where both coherent and incoherent states coexist. We investigate …

Finite-size scaling, dynamic fluctuations, and hyperscaling relation in the Kuramoto model

H Hong, H Chaté, LH Tang, H Park - Physical Review E, 2015‏ - APS
We revisit the Kuramoto model to explore the finite-size scaling (FSS) of the order parameter
and its dynamic fluctuations near the onset of the synchronization transition, paying …

Emergent behaviour of a generalized Viscek-type flocking model

SY Ha, E Jeong, MJ Kang - Nonlinearity, 2010‏ - iopscience.iop.org
We present a planar agent-based flocking model with a distance-dependent communication
weight. We derive a sufficient condition for the asymptotic flocking in terms of the initial …

Determination of the critical coupling of explosive synchronization transitions in scale-free networks by mean-field approximations

TKDM Peron, FA Rodrigues - Physical Review E—Statistical, Nonlinear, and …, 2012‏ - APS
An explosive synchronization can be observed in scale-free networks when Kuramoto
oscillators have natural frequencies equal to their number of connections. The present paper …

Criterion for the emergence of explosive synchronization transitions in networks of phase oscillators

L Zhu, L Tian, D Shi - Physical Review E—Statistical, Nonlinear, and Soft …, 2013‏ - APS
The emergence of explosive synchronization transitions in networks of phase oscillators
recently has become one of the most interesting topics. It is widely believed that the large …

Transition to collective oscillations in finite Kuramoto ensembles

F Peter, A Pikovsky - Physical Review E, 2018‏ - APS
We present an alternative approach to finite-size effects around the synchronization
transition in the standard Kuramoto model. Our main focus lies on the conditions under …

Critical behavior of the relaxation rate, the susceptibility, and a pair correlation function in the Kuramoto model on scale-free networks

S Yoon, M Sorbaro Sindaci, AV Goltsev, JFF Mendes - Physical Review E, 2015‏ - APS
We study the impact of network heterogeneity on relaxation dynamics of the Kuramoto
model on uncorrelated complex networks with scale-free degree distributions. Using the Ott …