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This study compares the Kuramoto model on 2D lattices and power grids, finding power grids exhibit earlier phase synchronization breakdown but less hysteresis. Network size, not self-organization, influences synchronization dynamics.

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Area of Science:

  • Complex Systems
  • Network Science
  • Statistical Physics

Background:

  • The Kuramoto model is a fundamental tool for studying synchronization phenomena in coupled oscillator systems.
  • Real-world networks, such as power grids, exhibit complex structures (weighted, hierarchical, modular) that differ significantly from simple lattices.
  • Inertia in power grids introduces first-order synchronization transitions, characterized by hysteresis and fast relaxation.

Purpose of the Study:

  • To compare the phase synchronization transition of the second-order Kuramoto model on 2D lattices versus real-world power grid networks.
  • To investigate the impact of network structure and inertia on synchronization dynamics and phase transitions.
  • To analyze the behavior of desynchronization avalanches and their underlying mechanisms.

Main Methods:

  • Simulations of the second-order Kuramoto model on 2D lattices and synthetic power grid networks.
  • Analysis of finite-size scaling to determine the presence of phase transitions in the thermodynamic limit.
  • Investigation of order parameter fluctuations and temporal behavior of desynchronization avalanches.
  • Characterization of network properties including weights, hierarchy, and modularity.

Main Results:

  • Synchronization transitions in power grids are of first-order type due to inertia, showing hysteresis.
  • Unlike mean-field models, no true phase transition exists in the thermodynamic limit for either network type.
  • Power grids exhibit phase synchronization breakdown at lower couplings than 2D lattices, with narrower or negligible hysteresis due to low connectivity.
  • Desynchronization avalanches display power-law duration distributions, indicating rare region effects from frozen disorder.

Conclusions:

  • Network topology and inertia significantly alter synchronization dynamics compared to simple lattice or mean-field models.
  • The absence of a true phase transition in the thermodynamic limit highlights the importance of finite-size effects.
  • Power grid networks demonstrate unique synchronization behaviors, including earlier breakdown and avalanche dynamics influenced by their specific structure and disorder.