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Universality Classes of Synchronization Phase Transitions

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Statistical Physics".

Deadline for manuscript submissions: 19 May 2025 | Viewed by 1880

Special Issue Editors


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Guest Editor
Centre for Energy Research, Institute of Technical Physics and Materials Science, P.O. Box 49, H-1525 Budapest, Hungary
Interests: nonequilibrium phase transitions; critical universality classes; disordered systems; brain network models; power-grid network models; surface growth classes

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Guest Editor Assistant
School of Physics and Information Technology, Shaanxi Normal University, Xi’an 710062, China
Interests: universality classes; phase transitions and scaling in non-equilibrium systems; field theoretical methods; renormalization group; statistical physics; complex systems; synchronization dynamics

Special Issue Information

Dear Colleagues,

Critical universality classes of non-equilibrium models, mainly of the reaction-diffusion type, are a well-explored area of statistical physics [1-3]. Much less is know about oscillatory models, which can also exhibit various types of phase transitions. Synchronization transitions are very ubiquitous in nature, and biological, neural, or power-grid systems are posed to be at the edge of such transitions. The behavior of such systems depends on the type of self-frequency, which acts as a quenched disorder.

In this Special Issue we collect articles on recent advances related to the synchronization transitions on a pathway of exploring universality classes of oscillatory models.

[1] Odor, G. Universality classes in nonequilibrium lattice systems. Rev. Mod. Phys. 2004, 76, 663.
[2] Odor, G. Universality in Nonequilibrium Lattice Systems, Theoretical Foundations; World Scientific: Singapore, 2008.
[3] Henkel, M.; Hinrichsen, H.; Lubeck, S. Nonequilibrium Phase Transitions; Springer: Berlin/Heidelberg, Germany, 2008.

Dr. Géza Ódor
Dr. Shengfeng Deng
Guest Editors

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Published Papers (2 papers)

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Research

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10 pages, 335 KiB  
Article
Frustrated Synchronization of the Kuramoto Model on Complex Networks
by Géza Ódor, Shengfeng Deng and Jeffrey Kelling
Entropy 2024, 26(12), 1074; https://doi.org/10.3390/e26121074 - 9 Dec 2024
Cited by 2 | Viewed by 801
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Universality Classes of Synchronization Phase Transitions)
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Review

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14 pages, 2627 KiB  
Review
Synchronization of Kuromoto Oscillators on Simplicial Complexes: Hysteresis, Cluster Formation and Partial Synchronization
by Samir Sahoo and Neelima Gupte
Entropy 2025, 27(3), 233; https://doi.org/10.3390/e27030233 - 24 Feb 2025
Viewed by 458
Abstract
The analysis of the synchronization of oscillator systems based on simplicial complexes presents some interesting features. The transition to synchronization can be abrupt or smooth depending on the substrate, the frequency distribution of the oscillators and the initial distribution of the phase angles. [...] Read more.
The analysis of the synchronization of oscillator systems based on simplicial complexes presents some interesting features. The transition to synchronization can be abrupt or smooth depending on the substrate, the frequency distribution of the oscillators and the initial distribution of the phase angles. Both partial and complete synchronization can be seen as quantified by the order parameter. The addition of interactions of a higher order than the usual pairwise ones can modify these features further, especially when the interactions tend to have the opposite signs. Cluster synchronization is seen on sparse lattices and depends on the spectral dimension and whether the networks are mixed, sparse or compact. Topological effects and the geometry of shared faces are important and affect the synchronization patterns. We identify and analyze factors, such as frustration, that lead to these effects. We note that these features can be observed in realistic systems such as nanomaterials and the brain connectome. Full article
(This article belongs to the Special Issue Universality Classes of Synchronization Phase Transitions)
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