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Asymmetry in the Kuramoto model with nonidentical coupling
M Elaeva1, E Blanter2, M Shnirman2
1Department of Higher Mathematics, HSE University, Moscow 109028, Russia.
Physical Review. E
|July 19, 2023
Summary
This study introduces a novel method to characterize oscillator synchronization without needing network coupling details. The asymmetry parameter (A) effectively predicts synchronization boundaries and can forecast solar cycle anomalies.
Area of Science:
- Physics
- Complex Systems
- Astrophysics
Background:
- Synchronization is crucial in many physical systems, but predicting it often requires detailed network structure.
- Existing methods struggle when coupling coefficients are unknown, common in natural sciences.
Purpose of the Study:
- To develop a method for characterizing oscillator synchronization without reconstructing network coupling.
- To introduce a new parameter, asymmetry (A), as a measure of synchronization.
Main Methods:
- Utilizing a Kuramoto chain model with three oscillators and non-identical coupling.
- Defining coupling by strength (s) and disparity (σ).
- Deriving an analytical expression for the synchronization boundary (s_max) and exploring scaling properties of asymmetry (A).
Main Results:
- An analytical expression for the synchronization boundary (s_max) was derived.
- Asymmetry (A) was proposed as a new characteristic of synchronization, found to be maximal at s_max.
- The interrelation between asymmetry (A) and synchronization was maintained across different network structures.
Conclusions:
- The asymmetry parameter (A) provides a robust way to characterize synchronization even without full network information.
- Asymmetry (A) can be derived from phase differences and applied to real-world data, such as solar magnetic field proxies.
- This method holds potential for forecasting solar cycle anomalies.
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