Ultrafast synchronization via local observation

Abstract

This paper proposes a Hankel matrix-based statistical study to calculate the final synchronization state of the entire network via local observation of just a single node for a time period significantly shorter than the synchronization process. It surfaces that synchronization can be achieved more quickly than the routine rhythm for networks no matter with linear or nonlinear dynamics. This finding refines our understanding of the abundant ultrafast synchronization phenomena observed in nature, which enables the efficient design of self-aligned robots as well.