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Time-delayed spatial patterns in a two-dimensional array of coupled oscillators.

Seong-Ok Jeong1, Tae-Wook Ko, Hie-Tae Moon

  • 1Department of Physics, Korea Advanced Institute of Science and Technology, Taejon 305-701, Korea.

Physical Review Letters
|October 9, 2002
PubMed
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Time delays in coupled phase oscillators create diverse patterns like spirals and targets. The study analyzes pattern stability and potential real-world applications of these distance-dependent effects.

Area of Science:

  • Complex systems
  • Nonlinear dynamics
  • Physics of oscillations

Background:

  • Coupled phase oscillators are fundamental models for synchronization phenomena.
  • Time delays are crucial factors influencing the dynamics of coupled systems.
  • Understanding pattern formation in oscillatory networks is key to many scientific fields.

Purpose of the Study:

  • To investigate the impact of distance-dependent time delays on pattern formation in two-dimensional coupled phase oscillators.
  • To identify and characterize the types of spatial patterns that emerge under varying delay conditions.
  • To analyze the stability of these induced patterns and explore their empirical relevance.

Main Methods:

  • Simulations of two-dimensional coupled phase oscillators with finite interaction radii.

Related Experiment Videos

  • Introduction of distance-dependent time delays as a control parameter.
  • Analysis of emergent spatial patterns, including traveling rolls, squares, rhombi, spirals, and targets.
  • Stability analysis of the observed patterns.

    • Main Results:

    • Distance-dependent time delays were shown to induce a rich variety of spatial patterns.
    • Observed patterns include traveling rolls, squarelike, rhombuslike, spirals, and target patterns.
    • The finite interaction radius and time delays significantly influence the configuration and stability of these patterns.

    Conclusions:

    • Time delays are a critical factor in determining the emergent behavior and spatial organization of coupled oscillator networks.
    • The identified patterns and their stability boundaries offer insights into complex system dynamics.
    • The findings suggest potential empirical implications in fields where coupled oscillatory behavior and spatial patterns are observed.