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Synchronization law for a van der Pol array.

Slaven Peles1, Kurt Wiesenfeld

  • 1Center for Nonlinear Science, School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332-0430, USA. peles@cns.physics.gatech.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 4, 2003
PubMed
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This study analyzes in-phase synchronization in coupled oscillator arrays, comparing van der Pol and Josephson junction systems. Josephson arrays differ fundamentally due to lacking self-resonant interactions, impacting synchronization dynamics.

Area of Science:

  • Nonlinear dynamics and complex systems.
  • Physics of coupled oscillators.
  • Array synchronization phenomena.

Background:

  • Globally coupled oscillator arrays are crucial in various scientific fields.
  • Understanding in-phase synchronization transitions is key to predicting system behavior.
  • Previous models often lack analytical tractability for complex arrays.

Purpose of the Study:

  • To investigate the transition to in-phase synchronization in globally coupled oscillator arrays.
  • To compare the synchronization dynamics of van der Pol oscillator arrays and Josephson junction arrays.
  • To develop analytically tractable models for these systems.

Main Methods:

  • Development of an analytically tractable iterative map for oscillator arrays.

Related Experiment Videos

  • Utilizing an expansion procedure to identify natural parameter groups.
  • Comparative analysis of van der Pol and Josephson junction array behaviors.

    • Main Results:

    • An iterative map was derived for both van der Pol and Josephson junction arrays.
    • Simple stability formulas were obtained by identifying natural parameter groups.
    • Duffing-van der Pol arrays share fundamental characteristics with van der Pol arrays.
    • Josephson junction arrays exhibit fundamental differences due to the absence of self-resonant interactions.

    Conclusions:

    • The developed iterative map provides a simplified analytical approach to synchronization studies.
    • The distinct behavior of Josephson junction arrays highlights the importance of self-resonant interactions.
    • This work offers insights into the fundamental mechanisms governing synchronization in diverse oscillator systems.