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Avalanches and scaling collapse in the large-N Kuramoto model
J Patrick Coleman1, Karin A Dahmen1, Richard L Weaver1
1Department of Physics, University of Illinois, 1110 West Green Street, Urbana, Illinois 61801, USA.
Physical Review. E
|May 16, 2018
Summary
We analyzed avalanches in the Kuramoto model, observing scaling behavior in avalanche dynamics. Our findings link this system to other driven avalanching systems, offering a comprehensive scaling picture.
Area of Science:
- Complex systems
- Statistical physics
- Nonlinear dynamics
Background:
- The Kuramoto model describes synchronization in populations of coupled oscillators.
- Avalanches, or rapid synchronization events, are a key phenomenon in this model.
- Understanding avalanche dynamics is crucial for characterizing complex systems.
Purpose of the Study:
- To investigate and characterize the scaling properties of avalanches in the Kuramoto model.
- To develop a comprehensive scaling picture of noise in the subcritical finite-N Kuramoto model.
- To connect the Kuramoto model's avalanching behavior to broader classes of driven systems.
Main Methods:
- Defining avalanches as order parameter excursions during synchronization episodes.
- Analyzing avalanche size, duration, height, and temporal profiles.
- Performing scaling collapses to extract critical exponents and scaling functions.
Main Results:
- Observed scaling collapses for various avalanche properties.
- Extracted scaling exponents and exponent relations consistent with theoretical predictions.
- Demonstrated consistency between avalanche scaling and power spectrum behavior.
Conclusions:
- A comprehensive scaling picture of noise in the subcritical finite-N Kuramoto model has been established.
- The study links the undriven Kuramoto model to driven avalanching systems.
- The findings provide insights into the universal scaling behavior of complex systems.
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