Synchronization in Network Geometries with Finite Spectral Dimension
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Publisher
Journal
Physical Review E
ISSN
1550-2376
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Show full item recordAbstract
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, GCollections
- Mathematics [236]