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Related Experiment Videos

Frequency synchronization in a random oscillator network.

Takashi Ichinomiya1

  • 1Meme Media Laboratory, Hokkaido University Sapporo, Hokkaido, Japan. miya@aurora.es.hokudai.ac.jp

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2004
PubMed
Summary

We investigated frequency synchronization in randomly coupled oscillators. A critical coupling constant of zero was found in scale-free networks for certain network structures, indicating synchronization is possible even with minimal coupling.

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Area of Science:

  • Complex systems
  • Nonlinear dynamics
  • Network science

Background:

  • Oscillator networks are fundamental to understanding emergent phenomena.
  • Frequency synchronization is a key collective behavior observed in various systems.
  • Scale-free networks exhibit unique topological properties influencing network dynamics.

Purpose of the Study:

  • To analyze the conditions for mean-field-type frequency synchronization in randomly coupled oscillators.
  • To investigate the impact of scale-free network topology on synchronization dynamics.
  • To determine the critical coupling constant for synchronization in these networks.

Main Methods:

  • Analysis of the continuum limit of coupled oscillator equations.
  • Derivation of a sufficient condition for mean-field synchronization.

Related Experiment Videos

  • Investigation of random scale-free networks with power-law degree distribution P(k) ~ k^(-gamma).
  • Numerical simulations on finite-sized networks.

    • Main Results:

    • A sufficient condition for mean-field-type synchronization was derived.
    • The critical coupling constant (K) was found to be zero for random scale-free networks when 2 < gamma <= 3.
    • Numerical simulations confirmed the analytical findings in finite networks.

    Conclusions:

    • Synchronization in randomly coupled oscillators is highly dependent on network topology.
    • Scale-free networks with specific degree distributions (2 < gamma <= 3) can exhibit synchronization even with vanishingly small coupling.
    • The study provides theoretical insights and numerical validation for synchronization phenomena in complex networks.