The Kuramoto model in complex networks

Author(s)

Rodrigues, Francisco A. ^[1] ; Peron, Thomas K. D. M. ^{[2, 3]} ; Ji, Peng ^{[2, 4]} ; Kurths, Juergen ^{[2, 4, 5, 6]}

Affiliation

^[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Dept Matemat Aplicada & Estat, Caixa Postal 668, BR-13560970 Sao Paulo - Brazil

^[2] Potsdam Inst Climate Impact Res PIK, D-14473 Potsdam - Germany

^[3] Univ Sao Paulo, Inst Fis Sao Carlos, Caixa Postal 369, BR-13560970 Sao Paulo - Brazil

^[4] Humboldt Univ, Dept Phys, D-12489 Berlin - Germany

^[5] Univ Aberdeen, Inst Complex Syst & Math Biol, Aberdeen AB24 3UE - Scotland

^[6] Nizhnii Novgorod State Univ, Dept Control Theory, Gagarin Ave 23, Nizhnii Novgorod 606950 - Russia

• Document type: Review article
• Source: PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS; v. 610, p. 1-98, JAN 26 2016.
• Web of Science Citations: 174

Abstract

Synchronization of an ensemble of oscillators is an emergent phenomenon present in several complex systems, ranging from social and physical to biological and technological systems. The most successful approach to describe how coherent behavior emerges in these complex systems is given by the paradigmatic Kuramoto model. This model has been traditionally studied in complete graphs. However, besides being intrinsically dynamical, complex systems present very heterogeneous structure, which can be represented as complex networks. This report is dedicated to review main contributions in the field of synchronization in networks of Kuramoto oscillators. In particular, we provide an overview of the impact of network patterns on the local and global dynamics of coupled phase oscillators. We cover many relevant topics, which encompass a description of the most used analytical approaches and the analysis of several numerical results. Furthermore, we discuss recent developments on variations of the Kuramoto model in networks, including the presence of noise and inertia. The rich potential for applications is discussed for special fields in engineering, neuroscience, physics and Earth science. Finally, we conclude by discussing problems that remain open after the last decade of intensive research on the Kuramoto model and point out some promising directions for future research. (c) 2015 Elsevier B.V. All rights reserved. (AU)

• FAPESP's process: 12/22160-7 - Synchronization of Kuramoto Oscillators in Complex Networks
• Grantee: Thomas Kaue Dal Maso Peron
• Support Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 13/26416-9 - Modelling of dynamical processes in complex networks
• Grantee: Francisco Aparecido Rodrigues
• Support Opportunities: Regular Research Grants
• FAPESP's process: 15/02486-3 - Synchronization of Kuramoto oscillators in complex networks
• Grantee: Thomas Kaue Dal Maso Peron
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate