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Related Experiment Videos

Collective phase synchronization in locally coupled limit-cycle oscillators.

H Hong1, Hyunggyu Park, M Y Choi

  • 1Department of Physics, Chonbuk National University, Jeonju 561-756, Korea.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 17, 2004
PubMed
Summary

Collective behavior in coupled oscillators shows desynchronization in lower dimensions. However, higher dimensions (d=5, 6) reveal synchronized phases, establishing a critical dimension of four for phase synchronization.

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Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Statistical Physics

Background:

  • Understanding collective behavior in systems of coupled oscillators is fundamental to various scientific fields.
  • The influence of dimensionality on synchronization phenomena in oscillatory networks with intrinsic frequency disorder remains an active research area.

Purpose of the Study:

  • To investigate the phase synchronization properties of locally coupled limit-cycle oscillators with scattered intrinsic frequencies across different lattice dimensions.
  • To determine the lower critical dimension for the emergence of synchronized behavior in this specific oscillatory system.

Main Methods:

  • Linear analysis was employed to predict the system's behavior in lower dimensions.
  • Numerical simulations were conducted for higher dimensions (d=5 and d=6) to observe emergent phenomena.

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Main Results:

  • Linear analysis indicated complete desynchronization for dimensions up to d=4.
  • Numerical investigations for d=5 and d=6 revealed a continuous phase transition from a desynchronized to a synchronized state.
  • The lower critical dimension for phase synchronization in this system was identified as d(l)=4.

Conclusions:

  • The dimensionality of the lattice plays a crucial role in the collective behavior of coupled oscillators with disordered frequencies.
  • A transition to synchronized behavior occurs in dimensions higher than the critical dimension of four, driven by a continuous transition from a desynchronized state.