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Generalized coupling in the Kuramoto model.

G Filatrella1, N F Pedersen, K Wiesenfeld

  • 1CNR-INFM SuperMat Salerno and Department of Biological and Environmental Sciences, University of Sannio, Via Port'Arsa 11, I-82100, Benevento, Italy.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 16, 2007
PubMed
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We introduce a modified Kuramoto model for coupled oscillators, allowing for tunable phase transitions. This model explains experimental observations in Josephson junctions and laser arrays.

Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Condensed Matter Physics

Background:

  • The Kuramoto model is a standard framework for studying synchronization in coupled oscillator systems.
  • Experimental systems like Josephson junctions, laser arrays, and mechanical systems exhibit complex coupling dynamics.
  • Sequential activation of elements in these systems can alter effective coupling constants.

Purpose of the Study:

  • To propose a modified Kuramoto model that incorporates effective changes in coupling constants.
  • To investigate the possibility of first and second-order phase transitions in such systems.
  • To provide an analytically tractable model consistent with experimental observations.

Main Methods:

  • Analytical modification of the Kuramoto model to include a tunable coupling parameter.

Related Experiment Videos

  • Derivation of conditions for different orders of phase transitions.
  • Numerical simulations to validate analytical predictions and compare with experimental data.

    • Main Results:

    • The modified model is analytically tractable, allowing for precise predictions.
    • Both first and second-order phase transitions are shown to be possible.
    • The occurrence of transition order depends on a new parameter tuning oscillator coupling.
    • Numerical simulations align with analytical estimates.
    • Qualitative agreement is found with experimental data from coupled Josephson junctions.

    Conclusions:

    • The proposed modified Kuramoto model offers a robust framework for understanding synchronization with dynamic coupling.
    • The model successfully predicts diverse phase transition behaviors.
    • It provides a theoretical basis for experimental findings in coupled active systems.