Synchronization on higher-order networks

Network science has already been fruitful and confirmed effective on the description of real-world or abstract systems. An increasing number of researches and instances have successfully verified, however, that interactions in systems may occur among three, four, or even more components. The introduction of higher-order perspective brings an revolution on network science, and refreshes researchers’ understanding of synchronization. Hence, an overview is presented here in regard of synchronization on higher-order networks. We start from an introduction of how the higher-order networks are represented using algebraic tools. Then a series of landmark researches on synchronization are reviewed under circumstances of whether or not the dynamics contains control. Finally, we summarize our conclusions and propose our outlooks on expectations of future works.