The Kuramoto model: A simple paradigm for synchronization phenomena

Juan A. Acebrón, L. L. Bonilla, Conrad J. Pérez Vicente, Félix Ritort, and Renato Spigler
Rev. Mod. Phys. 77, 137 – Published 7 April 2005

Abstract

Synchronization phenomena in large populations of interacting elements are the subject of intense research efforts in physical, biological, chemical, and social systems. A successful approach to the problem of synchronization consists of modeling each member of the population as a phase oscillator. In this review, synchronization is analyzed in one of the most representative models of coupled phase oscillators, the Kuramoto model. A rigorous mathematical treatment, specific numerical methods, and many variations and extensions of the original model that have appeared in the last few years are presented. Relevant applications of the model in different contexts are also included.

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    DOI:https://doi.org/10.1103/RevModPhys.77.137

    ©2005 American Physical Society

    Authors & Affiliations

    Juan A. Acebrón*

    • Departamento de Automática, Universidad de Alcalá, Crta. Madrid-Barcelona, km 31.600, 28871 Alcalá de Henares, Spain

    L. L. Bonilla

    • Grupo de Modelización y Simulación Numérica, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Spain

    Conrad J. Pérez Vicente and Félix Ritort§

    • Department de Fisica Fonamental, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain

    Renato Spigler

    • Dipartimento di Matematica, Università di Roma Tre, Largo S. Leonardo Murialdo 1, 00146 Roma, Italy

    • *Electronic address: juan.acebron@uah.es
    • Electronic address: bonilla@ing.uc3m.es
    • Electronic address: conrad@ffn.ub.es
    • §Electronic address: ritort@ffn.ub.es
    • Electronic address: spigler@mat.uniroma3.it

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    Issue

    Vol. 77, Iss. 1 — January - March 2005

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