{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,25]],"date-time":"2026-07-25T14:26:39Z","timestamp":1784989599314,"version":"3.55.0"},"reference-count":28,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,12,9]],"date-time":"2024-12-09T00:00:00Z","timestamp":1733702400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003827","name":"National Research, Development, and Innovation Office NKFIH","doi-asserted-by":"publisher","award":["K146736"],"award-info":[{"award-number":["K146736"]}],"id":[{"id":"10.13039\/501100003827","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003827","name":"National Research, Development, and Innovation Office NKFIH","doi-asserted-by":"publisher","award":["GK202406016"],"award-info":[{"award-number":["GK202406016"]}],"id":[{"id":"10.13039\/501100003827","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Fundamental Research Funds for the Central Universities of China","award":["K146736"],"award-info":[{"award-number":["K146736"]}]},{"name":"Fundamental Research Funds for the Central Universities of China","award":["GK202406016"],"award-info":[{"award-number":["GK202406016"]}]}],"content-domain":{"domain":["www.mdpi.com"],"crossmark-restriction":true},"short-container-title":["Entropy"],"abstract":"<jats:p>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&gt;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.<\/jats:p>","DOI":"10.3390\/e26121074","type":"journal-article","created":{"date-parts":[[2024,12,9]],"date-time":"2024-12-09T10:11:47Z","timestamp":1733739107000},"page":"1074","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Frustrated Synchronization of the Kuramoto Model on Complex Networks"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9259-5352","authenticated-orcid":false,"given":"G\u00e9za","family":"\u00d3dor","sequence":"first","affiliation":[{"name":"Institute of Technical Physics and Materials Science, HUN-REN Centre for Energy Research, P.O. Box 49, H-1525 Budapest, Hungary"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1952-8599","authenticated-orcid":false,"given":"Shengfeng","family":"Deng","sequence":"additional","affiliation":[{"name":"School of Physics and Information Technology, Shaanxi Normal University, Xi\u2019an 710062, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1761-2591","authenticated-orcid":false,"given":"Jeffrey","family":"Kelling","sequence":"additional","affiliation":[{"name":"Institute for Radiation Physics, Helmholtz-Zentrum Dresden\u2013Rossendorf, P.O. Box 510119, 01314 Dresden, Germany"},{"name":"Faculty of Natural Sciences, Chemnitz University of Technology, Stra\u00dfe der Nationen 62, 09111 Chemnitz, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3366","DOI":"10.1523\/JNEUROSCI.2523-11.2012","article-title":"Ongoing Cortical Activity at Rest: Criticality, Multistability, and Ghost Attractors","volume":"32","author":"Deco","year":"2012","journal-title":"J. Neurosci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/j.physrep.2008.09.002","article-title":"Synchronization in complex networks","volume":"469","author":"Arenas","year":"2008","journal-title":"Phys. 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