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Correction: Ódor et al. Frustrated Synchronization of the Kuramoto Model on Complex Networks. <i>Entropy</i> 2024, <i>26</i>, 1074.

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Frustrated Synchronization of the Kuramoto Model on Complex Networks.

Géza Ódor1, Shengfeng Deng2, Jeffrey Kelling3,4

  • 1Institute of Technical Physics and Materials Science, HUN-REN Centre for Energy Research, P.O. Box 49, H-1525 Budapest, Hungary.

Entropy (Basel, Switzerland)
|January 8, 2025
PubMed
Summary
This summary is machine-generated.

We studied synchronization transitions in the Kuramoto model on large networks. Network heterogeneity causes frustrated synchronization, differing from regular lattices.

Keywords:
Kuramotocriticalityspectral dimensionsynchronization

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Area of Science:

  • Complex systems
  • Network science
  • Statistical physics

Background:

  • The Kuramoto model is a standard framework for studying synchronization phenomena in coupled oscillator systems.
  • Understanding synchronization transitions in large and complex networks is crucial for various scientific domains.
  • Heterogeneous networks with long-range connections can exhibit distinct dynamical behaviors compared to regular lattices.

Purpose of the Study:

  • To investigate the synchronization transition of the locally coupled Kuramoto model on extremely large regular lattices and heterogeneous networks with power-law decaying long links.
  • To compare the critical behavior and scaling properties of synchronization in these different network structures.
  • To elucidate the role of network heterogeneity in synchronization dynamics.

Main Methods:

  • Simulations of the Kuramoto model on large regular lattices (405x405 and 1004x1004) and heterogeneous networks (12,000x12,000) with power-law decaying long links.
  • Analysis of synchronization transition using concepts of spectral dimensions (ds) and corrections to scaling.
  • Comparison of mean-field and non-mean-field critical behaviors.

Main Results:

  • Regular lattices show mean-field criticality with logarithmic corrections at d=4 and strong corrections at d=5 spectral dimensions.
  • Heterogeneous networks with long links exhibit a non-mean-field smeared transition with oscillating corrections at high spectral dimensions (ds>4).
  • Network heterogeneity significantly alters synchronization dynamics, leading to frustrated synchronization.

Conclusions:

  • The heterogeneity of networks with long links is a crucial factor influencing synchronization transitions.
  • The observed frustrated synchronization in heterogeneous networks resembles Griffiths effects.
  • This study highlights the importance of network topology in determining collective dynamics and phase transitions.