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Summary
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We investigated how phase shifts affect synchronization in complex networks using the Kuramoto model. Introducing repulsive coupling near a phase lag of π creates a novel "repulsive synchronization" pattern.

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Area of Science:

  • Complex Networks
  • Nonlinear Dynamics
  • Statistical Physics

Background:

  • Synchronization is a key phenomenon in complex autonomous systems, where coupled oscillators achieve phase-locking.
  • The Kuramoto model is a standard framework for studying synchronization transitions in networks.
  • Phase shifts in oscillator coupling can significantly alter synchronization dynamics.

Purpose of the Study:

  • To investigate the influence of a tunable phase-lag parameter (α) on synchronization transitions in the Kuramoto model.
  • To identify and characterize novel synchronization patterns induced by phase shifts, particularly repulsive coupling.

Main Methods:

  • Simulations of the Kuramoto model with a tunable phase-lag parameter α.
  • Analysis of synchronization transitions under varying coupling strengths and phase-lag values.
  • Introduction of the frequency dispersion parameter to detect synchronization, especially for patterns not captured by the standard order parameter r.

Main Results:

  • Phase frustration, introduced by the phase-lag parameter, can lead to desynchronization.
  • Two global synchronization regions were identified for α∈[0,2π) under sufficiently large coupling.
  • A rare synchronization pattern, termed 'repulsive synchronization,' was detected near α=π, induced by repulsive coupling.

Conclusions:

  • Phase shifts, particularly repulsive coupling, can induce unique synchronization behaviors like 'repulsive synchronization'.
  • The standard order parameter (r) is insufficient to describe repulsive synchronization, necessitating the use of frequency dispersion.
  • Understanding these phase-lag-induced dynamics is crucial for characterizing synchronization in diverse complex networks.