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Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Statistical Physics

Background:

  • Coupled oscillator models are crucial for understanding synchronization in natural and artificial systems.
  • The Kuramoto oscillator model is a fundamental framework for studying synchronization phenomena.
  • Higher-order interactions and parameters like phase lag and adaptation introduce complexity to synchronization dynamics.

Purpose of the Study:

  • To investigate the influence of phase lag and adaptation in higher-order interactions on the Kuramoto oscillator model.
  • To analyze how these parameters affect the order of synchronization transitions.
  • To explore the interplay between adaptation and phase lag in determining synchronization behavior.

Main Methods:

  • Numerical simulations of the coupled Kuramoto oscillator model.
  • Analysis of synchronization transitions (first-order, second-order, tiered synchronization).
  • Application of the Ott-Antonsen approach for analytical descriptions in the thermodynamic limit.

Main Results:

  • Synchronization transition order shifts from first-order to second-order, mediated by tiered synchronization, based on adaptation parameters.
  • Phase lag facilitates these transitions at lower adaptation parameter exponents.
  • The combined effect of adaptation and phase lag eliminates tiered synchronization, enabling a direct first-to-second-order transition.

Conclusions:

  • Adaptation and phase lag are key parameters controlling synchronization transition types in higher-order coupled oscillator systems.
  • The Ott-Antonsen approach provides accurate analytical predictions for synchronization dynamics, validated by numerical simulations.
  • This research deepens the understanding of synchronization mechanisms in complex systems.