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Effective-potential approach to hybrid synchronization transitions.

Je Ung Song¹, Jaegon Um^1,2, 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

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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.