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Related Experiment Video

Updated: Jun 14, 2026

Alignment of Synchronized Time-Series Data Using the Characterizing Loss of Cell Cycle Synchrony Model for Cross-Experiment Comparisons
07:59

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Published on: June 9, 2023

Structural properties of the synchronized cluster on complex networks.

Yup Kim1, Yongjin Ko, Soon-Hyung Yook

  • 1Department of Physics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Korea. ykim@khu.ac.kr

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 7, 2010
PubMed
Summary

The largest synchronized connected component (LSCC) forms by merging smaller clusters on complex networks. This study confirms mean-field percolation theory for LSCC formation on Erdős-Rényi and Barabási-Albert networks.

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Area of Science:

  • Complex network dynamics
  • Synchronization phenomena
  • Statistical physics

Background:

  • Understanding global synchronization in complex networks is crucial for various systems.
  • The Kuramoto model is a standard framework for studying synchronization.
  • The formation and evolution of the largest synchronized connected component (LSCC) remain key research questions.

Purpose of the Study:

  • To investigate the formation and evolution mechanisms of the LSCC in complex networks.
  • To analyze LSCC dynamics using the Kuramoto model on Erdős-Rényi and Barabási-Albert networks.
  • To compare findings with established theories like mean-field percolation.

Main Methods:

  • Finite-size scaling analysis applied to network synchronization.
  • Examination of percolation order parameter and mean cluster size.
  • Analysis of cluster size distributions and merging dynamics.

Main Results:

  • Scaling exponents for percolation order parameter and mean cluster size match mean-field percolation theory (β=γ=1).
  • Finite-size scaling exponent (ν) also aligns with mean-field percolation results (ν=3).
  • Cluster size distributions on both network types are identical to the mean-field percolation distribution.

Conclusions:

  • The LSCC on Erdős-Rényi and Barabási-Albert networks evolves through the merging of various-sized clusters.
  • Findings support the applicability of mean-field percolation theory to synchronization phenomena on these complex networks.
  • The study provides direct evidence for cluster merging as the primary mechanism for LSCC formation and global synchronization.