Equivalence of synchronization states in the Kuramoto flow: a unified framework
arXiv:2503.19781 · doi:10.1088/2632-072X/ae6be3
Abstract
On the fiftieth anniversary of the Kuramoto model, synchronization remains a central paradigm for collective behavior in complex oscillator systems. While phase locking, frequency synchronization, and order-parameter coherence are widely used to characterize synchronization, their precise dynamical relationship has remained unclear, especially in finite-dimensional systems beyond mean-field limits. In this work, we show that, in the fully connected Kuramoto model, full phase locking, phase locking, frequency synchronization, and order-parameter synchronization are dynamically equivalent. Moreover, we demonstrate that the equivalence between phase locking and frequency synchronization is governed by a topology-independent mechanism and persists for generic symmetric coupling structures. These results provide a unified dynamical framework for synchronization and clarify the structural role of the Kuramoto order parameter.
arXiv comment32 pages, 9 figures. Title and abstract updated to match the published version
References in corpus (9)
- Synchronization in Complex Oscillator Networks and Smart Grids
- Stability diagram for the forced Kuramoto model
- Fully Synchronous Solutions and the Synchronization Phase Transition for the Finite N Kuramoto Model
- Synchronization and Stability for Quantum Kuramoto
- Describing synchronization and topological excitations in arrays of magnetic spin torque oscillators through the Kuramoto model
- Asymptotic phase-locking dynamics and critical coupling strength for the Kuramoto model
- A Matrix Valued Kuramoto Model
- Synchrony for weak coupling in the complexified Kuramoto model
- Synchronization in the complexified Kuramoto model