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Related Experiment Videos

Regular and chaotic phase synchronization of coupled circle maps.

Grigory V Osipov1, Jürgen Kurths

  • 1Institute of Physics, University Potsdam 10, Am Neuen Palais, D-14415, Potsdam, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 22, 2002
PubMed
Summary

This study explores phase synchronization in coupled circle maps, revealing key factors influencing chaotic and regular synchronization. Synchronization regions typically shrink as phase evolution becomes less coherent.

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Area of Science:

  • Complex Systems Dynamics
  • Nonlinear Dynamics and Chaos
  • Statistical Physics

Background:

  • Phase synchronization is a fundamental phenomenon in coupled nonlinear oscillators.
  • Understanding synchronization in nonidentical systems is crucial for modeling complex networks.
  • Circle maps (CMs) provide a simplified yet powerful model for studying synchronization phenomena.

Purpose of the Study:

  • To investigate the effects of regular and chaotic phase synchronization in ensembles of coupled nonidentical circle maps.
  • To identify the key parameters governing synchronization in both regular and chaotic regimes.
  • To analyze the transitions to global synchronization in coupled CMs with varying frequency distributions.

Main Methods:

  • Analysis of phase-locking regions in ensembles of coupled nonidentical circle maps.

Related Experiment Videos

  • Quantification of synchronization based on rotation number difference, phase evolution variance, and interval dynamics.
  • Examination of soft and hard transitions to global synchronization in linear and random frequency distributions.

    • Main Results:

    • Phase-locking regions were identified for both regular and chaotic phase synchronization.
    • Chaotic synchronization is influenced by rotation number difference, phase variance, and interval dynamics; regular synchronization depends on variance and rotation number difference.
    • Increased noncoherence generally decreases the main (1:1) synchronization regions for both regimes.
    • Chaotic synchronization without bifurcations of the chaotic set was observed.
    • Soft and hard transitions to global synchronization were found in CM ensembles.

    Conclusions:

    • The study elucidates the distinct and overlapping factors controlling regular and chaotic phase synchronization in coupled CMs.
    • Noncoherence plays a critical role in diminishing synchronization regions.
    • The findings offer insights into the complex dynamics of coupled systems and transitions to global synchronization.