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Propagating structures in globally coupled systems with time delays

Zanette1

  • 1Consejo Nacional de Investigaciones Cientificas y Tecnicas, Centro Atomico Bariloche and Instituto Balseiro, 8400 Bariloche, Argentina.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
Summary

Globally coupled phase oscillators with finite-speed interactions synchronize in frequency. Spatial phase distributions emerge, forming propagating structures in one-dimensional arrays.

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Area of Science:

  • Physics
  • Complex Systems
  • Nonlinear Dynamics

Background:

  • Phase oscillators are fundamental in modeling coupled systems.
  • Finite interaction speeds introduce time delays, impacting system dynamics.
  • Spatial aspects are often neglected in globally coupled oscillator models.

Purpose of the Study:

  • To investigate the synchronization behavior of globally coupled phase oscillators with finite-speed interactions.
  • To analyze the emergence and nature of spatial phase distributions under time-delayed coupling.
  • To explore the dynamics of these distributions in specific geometries, such as 1D arrays.

Main Methods:

  • Analytical treatment in the limit of short time delays.
  • Numerical simulations on one-dimensional arrays of phase oscillators.

Related Experiment Videos

  • Analysis of frequency synchronization and spatial phase distribution.

    • Main Results:

    • The ensemble of oscillators achieves frequency synchronization.
    • A nontrivial, non-uniform distribution of phases over space develops.
    • In 1D arrays, this phase distribution manifests as a propagating structure.

    Conclusions:

    • Finite interaction speed is crucial for spatial effects in globally coupled oscillator ensembles.
    • Frequency synchronization is a key emergent behavior under time-delayed coupling.
    • Propagating spatial phase structures are a novel phenomenon in these systems.