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Relaxation dynamics of phase oscillators with generic heterogeneous coupling
Can Xu1, Xin Jin2, Yonggang Wu3
1Institute of Systems Science and College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China.
Physical Review. E
|March 18, 2023
Summary
This study explores how heterogeneity in coupled phase oscillators affects synchronization. We found that while the synchronization threshold is robust to inhomogeneity location, the correlation function critically influences dynamics and relaxation behavior.
Area of Science:
- Complex Systems
- Statistical Mechanics
- Nonlinear Dynamics
Background:
- Coupled phase oscillator models are key to understanding collective dynamics in large systems.
- Synchronization transitions in homogeneous systems are well-understood.
- Heterogeneous patterns in phase oscillators are increasingly important.
Purpose of the Study:
- Investigate the impact of quenched disorder in natural frequencies and coupling on oscillator synchronization.
- Analyze the role of correlation functions between heterogeneity types.
- Develop analytical methods for equilibrium states.
Main Methods:
- Utilized a variant of the Kuramoto model with quenched disorder.
- Correlated frequency and coupling heterogeneity using a weighted function.
- Developed an analytical treatment for equilibrium dynamics.
Main Results:
- Synchronization onset threshold is independent of inhomogeneity location but depends on the correlation function's center value.
- Relaxation dynamics from incoherent states are significantly shaped by heterogeneity.
- Out-coupling strategies facilitate synchronization in the supercritical region.
Conclusions:
- Heterogeneity plays a crucial role in the emergent dynamics of complex systems.
- Provides theoretical insights into statistical mechanical properties of steady states during synchronization.
- Highlights the importance of inhomogeneous patterns in understanding synchronization.
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