Fix-speed flocking of high-dimensional Kuramoto oscillator systems with proximity graph

Abstract

This paper examines the issue of flocking within a fixed-speed multi-agent system. Utilizing the high-dimensional Kuramoto model, it is demonstrated that given an initially connected proximity graph, the system can achieve flocking when the coupling intensity of the system exceeds a certain threshold. In this state, the proximity graph retains its connectivity, and no changes occur between agents over time. It is guaranteed that no collisions occur. Finally, the conclusion is substantiated with a straightforward example.