The Kuramoto model in complex networks

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• 作者：Francisco A. Rodrigues^a ; ^{francisco@icmc.usp.br" class="auth_mail" title="E-mail the corresponding author} ; Thomas K. DM. Peron^b ; ^c ; ^{thomaskaue@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Peng Ji^c ; ^d ; ^{pengji@pik-potsdam.de" class="auth_mail" title="E-mail the corresponding author} ; Jü ; rgen Kurths^c ; ^d ; ^e ; ^f ; ^{kurths@pik-potsdam.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：BA ; Barabá ; si&ndash ; Albert ; CM ; configuration model ; ER ; Erdős&ndash ; Ré ; nyi ; FPE ; Fokker&ndash ; Planck equation ; FSS ; finite-size scaling ; GA ; Gaussian approximation ; MFA ; mean-field approximation ; MSF ; master stability function ; OA ; Ott&ndash ; Antonsen ; PA ; preferential attachment ; SF ; scale-free ; SW ; small-world
• 刊名：Physics Reports
• 出版年：2016
• 出版时间：26 January 2016
• 年：2016
• 卷：610
• 期：Complete
• 页码：1-98
• 全文大小：7250 K

文摘

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.