Synchronization in Temporal Simplicial Complexes

The stability analysis of synchronization in time-varying higher-order networked structures (simplicial complexes) is one the challenging problem due to presence group interactions. In this context, most previous studies have been done either on temporal pairwise networks or static simplicial complexes. Here, for first time, we propose a general framework study phenomenon We show that synchronous state exists as an invariant solution and obtain necessary condition it be emerged stable fast switching regime. prove time-averaged complex plays role indicator whenever among topologies are adequately fast. attempt transform into master function form. Unfortunately, circumstances, dimension reduction equation cumbersome However, overcome difficulty two interesting situations based functional forms coupling schemes connectivity structure complex, demonstrate mimics form these cases. verify our analytical findings by applying them synthetic real-world systems. addition, results also reveal with sufficient rewiring, achieves synchrony even very low