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

TL;DR

This paper establishes a necessary and sufficient condition for achieving complete phase synchronization in high-dimensional nonidentical Kuramoto oscillators, expanding understanding of synchronization conditions in complex oscillator networks.

Contribution

It introduces a new theoretical criterion for complete phase synchronization in high-dimensional nonidentical Kuramoto models under strongly connected digraphs.

Findings

Synchronization is achievable under the derived condition.

Theoretical results are validated through simulations.

The condition applies to a broad class of high-dimensional models.

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.