Ultrafast Synchronization via Local Observation

Rapid expansions of their size and frequent changes of their topology make it difficult to observe and analyze complex networks. We explore the properties of the Hankel matrix and propose an algorithm for calculating the final synchronization state that uses a local observation of a single node for a time period significantly shorter than the synchronization process. We find that synchronization can be achieved more quickly than the routine rhythm. This finding refines our understanding of the abundant ultrafast synchronization phenomena observed in nature, and it enables the efficient design of self-aligned robots.