The influence of higher-order structure on the synchronization path of the network

Abstract

The influence of higher-order structures on network dynamic behaviors has gradually emerged as a significant focus in the field of network science. Among these behaviors, synchronization is a pivotal phenomenon. While existing studies primarily examine how higher-order structures affect synchronization types and thresholds, the dynamics of the synchronization process itself remain underexplored. In this work, we study the impact of higher-order BA network structures on ER random networks, specifically analyzing their effect on the synchronization path. Our findings reveal that introducing higher-order BA structures into ER random networks can either promote stepwise aggregation synchronization and hierarchical synchronization or suppress global synchronization, depending on the higher-order coupling strength. Moreover, as the higher-order coupling strength increases, when the higher-order BA network fails to synchronize, the ER structure can be employed to facilitate overall synchronization along the hierarchical synchronization path. The analysis presented in this paper reveals the complex influence of higher-order BA structures on network synchronization, offering new insights into the role of higher-order structures in network dynamics.