3 papers
math.DS2026
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,…
math.DS2025
Equivalence of Synchronization States in the Hybrid Kuramoto Flow
Ting-Yang Hsiao, Yun-Feng Lo, Chengbin Zhu
We establish a unified synchronization framework for the all-to-all hybrid Kuramoto model that couples first- and second-order oscillators within a single dynamical system. Althoug…
math.DS2025
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…