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Kinetic theory of coupled oscillators
Eric J Hildebrand1, Michael A Buice, Carson C Chow
1Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania, USA.
Physical Review Letters
|March 16, 2007
Summary
We describe system size effects in coupled oscillator networks using a novel hierarchy. This method accurately predicts fluctuations in the Kuramoto model, matching simulation results.
Area of Science:
- Complex systems
- Statistical physics
- Nonlinear dynamics
Background:
- The Kuramoto model describes synchronization in coupled oscillators but often neglects finite system size effects.
- Finite system size can induce correlations and alter dynamics, particularly near phase transitions.
Purpose of the Study:
- To develop a theoretical framework for describing fluctuations arising from finite system size effects in the Kuramoto model.
- To quantify the impact of these correlations on the order parameter fluctuations.
Main Methods:
- Constructed a moment hierarchy analogous to the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy.
- Truncated the hierarchy at second order to obtain closed equations for the two-oscillator correlation function.
- Computed order parameter fluctuations, including transient effects, using the derived correlation function.
Main Results:
- The derived hierarchy provides a systematic approach to account for system size effects.
- The second-order truncation successfully captures the lowest-order system size corrections.
- Theoretical predictions for order parameter fluctuations show good agreement with numerical simulations.
Conclusions:
- The proposed method offers an effective way to analyze finite size effects in coupled oscillator systems.
- This approach enhances the understanding of fluctuations and transient dynamics in the Kuramoto model.
- The findings are relevant for various fields employing coupled oscillator models.
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