2022•arXiv (Cornell University)Open access

A Necessary and Sufficient Condition for Complete phase synchronization of high-dimensional nonidentical Kuramoto oscillators

Yushi Shi, Ting Li, Jiandong Zhu

Abstract

For original Kuramoto models with nonidentical oscillators, it is impossible to realize complete phase synchronization. However, this paper reveals that complete phase synchronization can be achieved for a large class of high-dimensional Kuramoto models with nonidentical oscillators. Under the topology of strongly connected digraphs, a necessary and sufficient condition for complete phase synchronization is obtained. Finally, some simulations are provided to validate the obtained theoretic results.

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Key concepts: Synchronization (alternating current), Kuramoto model, Synchronization networks, Topology (electrical circuits), Phase synchronization, Phase (matter), Computer science, Class (philosophy)