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Finite-size effects in Kuramoto oscillator systems with higher-order interactions cause synchronization transitions earlier than predicted. These effects also lead to new partially synchronized states not seen in larger systems.

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Area of Science:

  • Complex systems
  • Nonlinear dynamics
  • Statistical physics

Background:

  • Finite-size systems exhibit unique dynamics, particularly multi-stability with coexisting coherent and incoherent states.
  • The Kuramoto model is a standard framework for studying synchronization phenomena in coupled oscillators.

Purpose of the Study:

  • Investigate finite-size effects on synchronization transitions in globally coupled Kuramoto oscillators with higher-order interactions.
  • Explore the emergence of new dynamical states in finite-size two-population oscillator systems.

Main Methods:

  • Numerical simulations of the Kuramoto model with higher-order interactions.
  • Analysis of the first exit-time distribution of the order parameter magnitude.
  • Calculation of numerical transition probabilities for varying system sizes.
  • Examination of the velocity field of order parameters in a two-population system.

Main Results:

  • Finite-size fluctuations drive earlier synchronization transitions compared to the thermodynamic limit.
  • A new fixed point, representing a partially synchronized state, emerges in finite-size two-population systems.
  • This partially synchronized state is absent in the thermodynamic limit.

Conclusions:

  • Finite-size effects significantly alter synchronization dynamics and can lead to novel emergent states.
  • Understanding these effects is crucial for accurately modeling real-world complex systems with limited components.