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    Exotic equilibria of Harary graphs and a new minimum degree lower bound for synchronization

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    Type
    Article
    Authors
    Canale, Eduardo A.
    Monzón, Pablo cc
    Date
    2015-02
    Permanent link to this record
    http://hdl.handle.net/10754/598276
    
    Metadata
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    Abstract
    © 2015 AIP Publishing LLC. This work is concerned with stability of equilibria in the homogeneous (equal frequencies) Kuramoto model of weakly coupled oscillators. In 2012 [R. Taylor, J. Phys. A: Math. Theor. 45, 1-15 (2012)], a sufficient condition for almost global synchronization was found in terms of the minimum degree-order ratio of the graph. In this work, a new lower bound for this ratio is given. The improvement is achieved by a concrete infinite sequence of regular graphs. Besides, non standard unstable equilibria of the graphs studied in Wiley et al. [Chaos 16, 015103 (2006)] are shown to exist as conjectured in that work.
    Citation
    Canale EA, Monzón P (2015) Exotic equilibria of Harary graphs and a new minimum degree lower bound for synchronization. Chaos: An Interdisciplinary Journal of Nonlinear Science 25: 023106. Available: http://dx.doi.org/10.1063/1.4907952.
    Sponsors
    This work was partially done during the scientific visit of the first author to the team of Raúl Tempone at KAUST (King Abdullah University of Science and Technology). We want to thank the anonymous referees for their useful comments and suggestions.
    Publisher
    AIP Publishing
    Journal
    Chaos: An Interdisciplinary Journal of Nonlinear Science
    DOI
    10.1063/1.4907952
    PubMed ID
    25725642
    ae974a485f413a2113503eed53cd6c53
    10.1063/1.4907952
    Scopus Count
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