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Finite-size effect in Kuramoto oscillators with higher-order interactions
1Complex Systems Lab, Department of Physics, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore 453552, India.
Chaos (Woodbury, N.Y.)
|October 11, 2024
Summary
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.
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.
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