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Topological speed limits to network synchronization.

Marc Timme1, Fred Wolf, Theo Geisel

  • 1Max-Planck-Institut für Strömungsforschung and Fakultät für Physik, Universität Göttingen, 37073 Göttingen, Germany.

Physical Review Letters
|March 5, 2004
PubMed
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We found that random matrix theory accurately predicts synchronization speed in pulse-coupled oscillator networks. Network connectivity limits this speed, ensuring finite synchronization even with infinite coupling.

Area of Science:

  • Complex systems
  • Network science
  • Nonlinear dynamics

Background:

  • Collective synchronization is crucial in various natural and engineered systems.
  • Understanding synchronization dynamics on complex networks is a significant challenge.
  • Asymmetric random networks present unique challenges for synchronization analysis.

Purpose of the Study:

  • To investigate collective synchronization in pulse-coupled oscillators on asymmetric random networks.
  • To develop a theoretical framework for predicting synchronization speed.
  • To explore the impact of network structure and coupling strength on synchronization.

Main Methods:

  • Utilizing random matrix theory to analyze network properties.
  • Developing analytical models for pulse-coupled oscillator dynamics.

Related Experiment Videos

  • Simulating oscillator networks to validate theoretical predictions.

    • Main Results:

    • Random matrix theory accurately predicts synchronization speed across various parameters.
    • Synchronization speed is fundamentally limited by network connectivity.
    • Finite synchronization speed is maintained even with infinite coupling strength.
    • Synchrony demonstrates robustness against structural perturbations.

    Conclusions:

    • Random matrix theory provides a powerful tool for understanding synchronization in complex networks.
    • Network connectivity is a critical determinant of synchronization speed.
    • The synchronization of pulse-coupled oscillators is resilient to dynamic and structural changes.