Synchronization of high‐dimensional Kuramoto models with nonidentical oscillators and interconnection digraphs

Abstract

This paper investigates some synchronization behaviors of high-dimensional Kuramoto models with nonidentical oscillators and interconnection digrphs. By using the matrix Riccati differential equation of the state error variables, it is proved that a high-dimensional Kuramoto model can achieve local practical synchronization when the interconnection digraph is strongly connected or has a spanning tree. Compared with the existing practical synchronization literature, the results are based on general digraphs instead of complete graphs. Moreover, the complete synchronization is proved for proportional nonidentical oscillators limited on a half-sphere and interconnected by a strongly connected digraph. Finally, some numerical simulations are given to validate the obtained theoretical results.

Asymptotic convergence of heterogeneous first-order aggregation models: from the sphere to the unitary group

“…We also refer the reader to [17] for similar results in the above when the underlying graph becomes a digraph containing a directed spanning tree.…”