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Updated: Jul 12, 2026
05:04
Bouncing Ball with a Uniformly Varying Velocity in a Metronome Synchronization Task
Published on: September 21, 2017
On the role of higher-order interactions toward first synchronization time
Dhrubajyoti Biswas1, Pintu Patra1, Arpan Banerjee2
1Indian Institute of Technology Kharagpur, Kharagpur, West Bengal 721302, India.
Chaos (Woodbury, N.Y.)
|July 10, 2026
Summary
Higher-order interactions in Kuramoto oscillator networks show complex effects on synchronization time. Increasing interaction order can initially speed up, then significantly slow down, the synchronization process.
Area of Science:
- Complex systems
- Nonlinear dynamics
- Statistical physics
Background:
- Kuramoto oscillators are a fundamental model for studying synchronization in coupled systems.
- Understanding transient dynamics and the impact of interaction complexity is crucial for various fields.
Purpose of the Study:
- To investigate how higher-order interactions influence the time to reach steady-state synchronization in Kuramoto oscillator ensembles.
- To analyze the effects of varying coupling strengths and interaction orders on synchronization dynamics.
Main Methods:
- Derivation of an expression for the first synchronization time using the Ott-Antonsen ansatz.
- Numerical simulations of globally coupled Kuramoto oscillators with Cauchy-distributed natural frequencies.
- Analysis of system dynamics through order-parameter evolution.
Main Results:
- Increasing coupling strength accelerates synchronization for a fixed interaction order.
- Increasing interaction order shows non-monotonic behavior: triadic interactions often accelerate synchronization, while further higher-order interactions progressively delay it.
- Very high interaction orders can lead to dynamics resembling pairwise interactions.
Conclusions:
- Higher-order interactions introduce significant complexity to synchronization dynamics, deviating from simple pairwise coupling effects.
- The interplay between coupling strength and interaction order dictates the convergence time to a synchronized state.
- The Ott-Antonsen ansatz and numerical simulations provide a robust framework for analyzing these complex collective behaviors.
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