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Updated: Dec 17, 2025
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Real-time Electrophysiology: Using Closed-loop Protocols to Probe Neuronal Dynamics and Beyond
Published on: June 24, 2015
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Effective-potential approach to hybrid synchronization transitions.
Je Ung Song1, Jaegon Um1,2, Jinha Park1
1CCSS, CTP and Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea.
Physical Review. E
|June 25, 2020
Summary
The Kuramoto model
Area of Science:
- Complex systems
- Nonlinear dynamics
- Statistical physics
Background:
- The Kuramoto model describes synchronization phenomena in coupled oscillators.
- The self-consistency equation (SCE) approach is limited in analyzing stability and detailed properties.
- Understanding synchronization transitions requires advanced analytical tools.
Purpose of the Study:
- To extend the Kuramoto self-consistency equation (SCE) approach.
- To introduce an effective potential for analyzing synchronization transitions.
- To investigate the effective potential landscape for different transition types.
Main Methods:
- Integral version of the Kuramoto self-consistency equation (SCE).
- Analysis of the effective potential landscape.
- Examination in the thermodynamic limit for various synchronization transitions.
Main Results:
- The effective potential landscape was analyzed for second-order, first-order, and hybrid synchronization transitions.
- A plateau in the effective potential minimum was observed during hybrid transitions.
- This plateau correlates with the order parameter jump in hybrid synchronization.
Conclusions:
- The effective potential method provides deeper insights into synchronization transitions.
- The effective potential can differentiate between transition types in the Kuramoto model.
- This approach enhances the understanding of oscillator synchronization dynamics.
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