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    Synchronization in Network Geometries with Finite Spectral Dimension 
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    Synchronization in Network Geometries with Finite Spectral Dimension

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    Accepted version (2.405Mb)
    Publisher
    American Physical Society
    Journal
    Physical Review E
    ISSN
    1550-2376
    Metadata
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    Abstract
    Recently there is a surge of interest in network geometry and topology. Here we show that the spectral dimension plays a fundamental role in establishing a clear relation between the topological and geometrical properties of a network and its dynamics. Specifically we explore the role of the spectral dimension in determining the synchronization properties of the Kuramoto model. We show that the synchronized phase can only be thermodynamically stable for spectral dimensions above four and that phase entrainment of the oscillators can only be found for spectral dimensions greater than two. We numerically test our analytical predictions on the recently introduced model of network geometry called Complex Network Manifolds which displays a tunable spectral dimension.
    Authors
    Millán, AP; Torres, JJ; Bianconi, G
    URI
    https://qmro.qmul.ac.uk/xmlui/handle/123456789/55228
    Collections
    • Mathematics [236]
    Licence information
    This is a pre-copyedited, author-produced version of an article accepted for publication in Physical Review E following peer review.
    Copyright statements
    © 2019 American Physical Society
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