Frustrated Synchronization of the Kuramoto Model on Complex Networks

Géza Ódor; Shengfeng Deng; Jeffrey Kelling

doi:10.20944/preprints202411.0382.v1

Preprint Article Version 1 This version is not peer-reviewed

Version 1 : Received: 5 November 2024 / Approved: 6 November 2024 / Online: 6 November 2024 (06:05:59 CET)

We present a synchronization transition study of the locally coupled Kuramoto model on extremely large graphs. We compare regular 405 and 1004 lattice results with those of 120002 lattice substrates with power-law decaying long links (ll). The latter heterogeneous network exhibits ds>4 spectral dimensions. We show strong corrections to scaling and mean-field type of criticality at d=5, while logarithmic corrections at d=4. Contrary, the ll model exhibits a non-mean field smeared transition, with oscillating corrections, suggesting the network heterogeneity is relevant, causing frustrated synchronization, akin to Griffiths effects.

synchronization; Kuramoto; criticality; spectral dimension

Physical Sciences, Theoretical Physics

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Frustrated Synchronization of the Kuramoto Model on Complex Networks

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