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Spatial correlations in a finite-range Kuramoto model.

Sebastian Wüster1, Rajasekaran Bhavna2

  • 1Department of Physics, Indian Institute of Science Education and Research, Bhopal, Madhya Pradesh 462 023, India.

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|June 25, 2020
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Summary
This summary is machine-generated.

We analyzed spatial correlations in the Kuramoto model to understand oscillator synchronization. Our findings reveal how interaction range and strength can be inferred from phase correlations, aiding biological system analysis.

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Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Systems Biology

Background:

  • The Kuramoto model describes synchronization in systems of coupled oscillators.
  • Spatial correlations are crucial for understanding local interactions in distributed systems, like cellular gene expression.
  • Limited interaction range and noise influence oscillator synchronization dynamics.

Purpose of the Study:

  • To analytically infer spatial phase-correlation functions in the Kuramoto model.
  • To determine if these correlations can reveal interaction range and strength.
  • To explore ergodicity for enabling temporal averaging in experimental measurements.

Main Methods:

  • Analytical derivation of spatial phase-correlation functions from steady-state oscillator distributions.
  • Development of a method to estimate system noise.
  • Simulations for both homogenous and heterogenous oscillator frequencies.
  • Comparison with experimental data from zebrafish segmentation clock.

Main Results:

  • Spatial phase-correlation functions analytically derived for homogenous frequencies.
  • Demonstrated that correlation functions contain information on interaction range and strength, contingent on noise estimation.
  • Identified conditions for ergodicity, allowing temporal averages for experimental measurements.
  • Simulations confirmed qualitative agreement for heterogenous frequencies.

Conclusions:

  • The study provides a framework for quantifying interaction parameters in spatially extended oscillator systems.
  • The developed methods are applicable to biological systems, such as gene expression oscillations.
  • Results are validated against experimental data, demonstrating practical relevance.