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4 papers
On the Equivalence of Synchronization Definitions in the Kuramoto Flow: A Unified Approach
Ting-Yang Hsiao, Yun-Feng Lo, Chengbin Zhu
We present a rigorous mathematical framework establishing the equivalence of four classical notions of synchronization full phase-locking, phase-locking, frequency synchronization,…
Synchronization and Hopf Bifurcation in Stuart--Landau Networks
Kuan-Wei Chen, Ting-Yang Hsiao
The Kuramoto model has shaped our understanding of synchronization in complex systems, yet its phase-only formulation neglects amplitude dynamics that are intrinsic to many oscilla…
Synchronization Relations in the Hybrid Kuramoto Flow: Equivalence and a High-Coherence Criterion
Ting-Yang Hsiao, Yun-Feng Lo, Chengbin Zhu
We study four synchronization notions for the all-to-all hybrid Kuramoto model containing both first- and second-order oscillators with heterogeneous inertias and damping coefficie…
Synchronization in the complexified Kuramoto model
Ting-Yang Hsiao, Yun-Feng Lo, Winnie Wang
In this paper, we consider an -oscillators complexified Kuramoto model. We first observe that there are solutions exhibiting finite-time blow-up behavior in all coupling regimes…