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Renormalization group approach to oscillator synchronization.

Oleg Kogan1, Jeffrey L Rogers, M C Cross

  • 1Department of Materials Science, California Institute of Technology, 1200 E California Boulevard, Pasadena, California 91125, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2009
PubMed
Summary
This summary is machine-generated.

We developed a renormalization group method to study synchronization clusters in disordered phase oscillator chains. This method accurately predicts cluster statistics and characteristic lengths, validated by numerical simulations.

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Area of Science:

  • Complex Systems
  • Statistical Physics
  • Nonlinear Dynamics

Background:

  • Synchronization phenomena are crucial in coupled oscillator systems.
  • Disorder in frequencies and couplings significantly impacts synchronization patterns.
  • Investigating synchronization clusters requires robust analytical and numerical tools.

Purpose of the Study:

  • To develop and apply a renormalization group (RG) method for analyzing synchronization clusters.
  • To investigate the effects of strong disorder in intrinsic frequencies and coupling strengths.
  • To analyze cluster statistics and characteristic lengths for Lorentzian distributions.

Main Methods:

  • Renormalization group (RG) method applied to a 1D chain of coupled phase oscillators.
  • Numerical simulations of the chain dynamics for comparison and validation.
  • Analysis of cluster size, frequency statistics, and characteristic length dependence on distribution parameters.

Main Results:

  • The RG method shows good agreement with numerical simulations for synchronization cluster characteristics.
  • The study successfully investigated cluster statistics under strong disorder.
  • The dependence of characteristic cluster length on Lorentzian distribution parameters was determined.

Conclusions:

  • The developed RG method is effective for studying synchronization clusters in disordered systems.
  • The findings provide insights into the statistical properties of synchronization clusters.
  • The research quantifies the impact of disorder on cluster formation and characteristics.