Emergent behaviors in the fractional Kuramoto model with general network topologies and its hybridization

We study the collective behaviors of the fractional Kuramoto model (FKM) proposed in [16] with general interaction network topologies and present a new hybrid fractional Kuramoto (HFKM) model for synchronization. Here, our proposed HFKM model consists of continuous evolution processes and a sequence of discrete processes. The continuous dynamics between discrete times is governed by the fractional Kuramoto (FKM) model, whereas a sequence of discrete processes governs the reinitialization of data by deleting past memory of phase dynamics except for the current state and changing interaction network topologies. For the proposed models, we provide sufficient conditions for the emergence of practical synchronization for nonidentical oscillators and phase synchronization for identical oscillators, respectively. This improves the earlier work [16] on the slow relaxation of the FKM model.