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Reentrant synchronization and pattern formation in pacemaker-entrained Kuramoto oscillators.

Filippo Radicchi1, Hildegard Meyer-Ortmanns

  • 1School of Engineering and Science, International University Bremen, P.O. Box 750561, D-28725 Bremen, Germany. f.radicchi@iu-bremen.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 10, 2006
PubMed
Summary

This study explores Kuramoto oscillator synchronization. A pacemaker can entrain oscillators, and systems with frequency gradients spontaneously develop a pacemaker, demonstrating novel synchronization dynamics.

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Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Complex Systems

Background:

  • Kuramoto oscillators are widely used to model synchronization in coupled systems.
  • Understanding phase entrainment is crucial for diverse fields, from neuroscience to power grids.
  • The role of interaction range and frequency distribution in synchronization remains an active research area.

Purpose of the Study:

  • To investigate phase entrainment in Kuramoto oscillators under varying interaction ranges and natural frequencies.
  • To analyze the effect of a pacemaker (impurity/defect) on oscillator synchronization.
  • To examine synchronization dynamics in systems with initial gradients in natural frequencies.

Main Methods:

  • Analytical derivation of entrainment frequency and threshold for specific coupling conditions.
  • Numerical simulations to explore synchronization transitions and reentrance phenomena.
  • Analysis of systems on one-dimensional chains and two-dimensional lattices.

Main Results:

  • Analytical solutions for entrainment frequency and threshold were derived.
  • A reentrance of the synchronization transition was observed as a function of coupling range, linked to coupling strength normalization.
  • In systems with frequency gradients, the oscillator with the highest natural frequency spontaneously acted as a pacemaker.

Conclusions:

  • The study provides analytical and numerical insights into Kuramoto oscillator synchronization.
  • Pacemaker-induced entrainment and self-organized pacemaker behavior were demonstrated.
  • Findings contribute to the understanding of synchronization phenomena in complex oscillatory systems.