Transition from Adler-type to event-driven synchronization in a self-organized rotating pulse

We investigate synchronization in a self-organized nonlinear pulse rotating on a ring. External synchronization is commonly classified into Adler-type synchronization, governed by continuous phase dynamics, and event-driven synchronization, dominated by discrete interactions. Their dynamical interplay within a single physical system, however, remains insufficiently understood. The rotating pulse system studied here provides a platform in which both mechanisms naturally emerge. Owing to dispersion, the pulse rotation velocity self-adjusts to match the external driving frequency. In the low-frequency regime, synchronization is governed by continuous Adler-type phase dynamics. As the driving frequency increases, the rotation velocity approaches its upper bound, leading to a dynamical connection to event-driven synchronization. This transition is accompanied by qualitative changes in phase statistics and rotation dynamics, demonstrating that hybrid synchronization behavior can arise intrinsically in a single distributed nonlinear system. From a dynamical systems perspective, the observed behavior may be interpreted as an effective connection between synchronization regimes. These findings provide insight into the fundamental structure of external synchronization in nonlinear wave-based oscillators.