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Synchronization on small-world networks.

H Hong1, M Y Choi, Beom Jun Kim

  • 1Department of Physics and Center for Theoretical Physics, Seoul National University, Seoul 151-747, Korea.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 28, 2002
PubMed
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Collective synchronization in coupled oscillators emerges with few shortcuts on small-world networks. Optimal phase synchronization is achieved with minimal network rewiring, similar to random networks.

Area of Science:

  • Complex systems
  • Network science
  • Nonlinear dynamics

Background:

  • Collective synchronization is a fundamental phenomenon in various natural and engineered systems.
  • Small-world networks exhibit unique topological properties, bridging regular and random networks.
  • Understanding synchronization dynamics on these networks is crucial for diverse applications.

Purpose of the Study:

  • To investigate the emergence and characteristics of collective synchronization in coupled oscillators on small-world networks.
  • To analyze the impact of network structure, specifically the fraction of shortcuts, on synchronization.
  • To quantify synchronization using order parameters for phases and frequencies.

Main Methods:

  • Dynamic simulations were employed to model the behavior of coupled oscillators.

Related Experiment Videos

  • Finite-size scaling analysis was used to characterize the transition to synchronization.
  • Order parameters were introduced to measure phase and frequency synchronization.

    • Main Results:

    • Phase synchronization emerges rapidly with a small fraction of shortcuts (P).
    • Synchronization saturates for shortcut fractions greater than or equal to 0.5.
    • Achieving high synchronizability comparable to random networks (P=1) requires fewer shortcuts.

    Conclusions:

    • Small-world network topology significantly enhances the ease of achieving collective synchronization.
    • Efficient synchronization can be attained in networks with a limited number of long-range connections.
    • The study provides insights into the transient dynamics and relaxation times associated with synchronization.