Frustrated Synchronization of the Kuramoto Model on Complex Networks

Ódor, Géza and Deng, Shengfeng and Kelling, Jeffrey (2024) Frustrated Synchronization of the Kuramoto Model on Complex Networks. ENTROPY, 26 (12). No.-1074. ISSN 1099-4300

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Abstract

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 12,0002 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, with logarithmic corrections at d=4 Euclidean dimensions. Contrarily, the ll model exhibits a non-mean-field smeared transition, with oscillating corrections at similarly high spectral dimensions. This suggests that the network heterogeneity is relevant, causing frustrated synchronization akin to Griffiths effects.

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