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Dynamics of phase oscillators with generalized frequency-weighted coupling.

Can Xu1,2, Jian Gao1,3, Hairong Xiang1

  • 1Department of Physics and the Beijing-Hong Kong-Singapore Joint Center for Nonlinear and Complex Systems (Beijing), Beijing Normal University, Beijing 100875, China.

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Summary

This study generalizes the Kuramoto model for heterogeneous coupling in oscillator networks. It provides a framework to understand synchronization transitions in complex systems with varying interaction strengths.

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Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Statistical Physics

Background:

  • Heterogeneous coupling is common in interacting systems across science.
  • Understanding synchronization in such systems is a key challenge.

Purpose of the Study:

  • To extend the Kuramoto model for heterogeneous coupling schemes.
  • To analyze synchronization transitions and predict system states.

Main Methods:

  • Generalized Kuramoto theory for heterogeneous couplings.
  • Self-consistency approach for stationary states.
  • Linear stability analysis and resonance poles theory.

Main Results:

  • Derived generalized expressions for critical coupling strength.
  • Developed a method to predict stationary states in the thermodynamic limit.
  • Revealed generic Landau damping effects below the critical threshold.

Conclusions:

  • Theoretical analysis and numerical results align, validating the extended model.
  • Provides a robust framework for understanding synchronization in general heterogeneous networks.