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Cluster Explosive Synchronization in Complex Networks

Peng Ji, Thomas K. DM. Peron, Peter J. Menck, Francisco A. Rodrigues, and Jürgen Kurths
Phys. Rev. Lett. 110, 218701 – Published 23 May 2013
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    Abstract

    The emergence of explosive synchronization has been reported as an abrupt transition in complex networks of first-order Kuramoto oscillators. In this Letter we demonstrate that the nodes in a second-order Kuramoto model perform a cascade of transitions toward a synchronous macroscopic state, which is a novel phenomenon that we call cluster explosive synchronization. We provide a rigorous analytical treatment using a mean-field analysis in uncorrelated networks. Our findings are in good agreement with numerical simulations and fundamentally deepen the understanding of microscopic mechanisms toward synchronization.

    • Received 22 January 2013

    DOI:https://doi.org/10.1103/PhysRevLett.110.218701

    © 2013 American Physical Society

    Authors & Affiliations

    Peng Ji1,2,*, Thomas K. DM. Peron3,†, Peter J. Menck1,2, Francisco A. Rodrigues4,‡, and Jürgen Kurths1,2,5

    • 1Potsdam Institute for Climate Impact Research (PIK), 14473 Potsdam, Germany
    • 2Department of Physics, Humboldt University, 12489 Berlin, Germany
    • 3Instituto de Física de São Carlos, Universidade de São Paulo, Avenida Trabalhador São Carlense 400, Caixa Postal 369, CEP 13560-970 São Carlos, São Paulo, Brazil
    • 4Departamento de Matemática Aplicada e Estatística, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Caixa Postal 668,13560-970 São Carlos, São Paulo, Brazil
    • 5Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom

    • *pengji@pik-potsdam.de
    • †thomas.peron@usp.br
    • ‡francisco@icmc.usp.br

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    Issue

    Vol. 110, Iss. 21 — 24 May 2013

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