Temporal evolution of intralayer synchronizability in multiplex hypergraphs

In practical applications, complex networks often model scenarios involving higher-order relationships, for which hypergraphs offer a suitable representation. This paper introduces synchronizability metrics to study the synchronization of a temporal two-layer multiplex hypergraph, where temporal characteristics are captured by time-evolving incidence matrix. By transforming hyperedges into maximal cliques, we construct a temporally evolving weighted network that reproduces the dynamics on the hypergraph under simple structure and symmetric coupling. The analysis focuses on intralayer synchronizability across different spatio-temporal scales. In the short term, we observe that the synchronizability of the hypergraph is positively correlated with network stochasticity. For the long term, we derive time-averaged approximation equations for fast-switching hypergraph and conduct both linear and global stability analyses to determine the necessary conditions for intralayer synchronization. Experimental results demonstrate that fast-switching hypergraph achieve superior long-term synchronizability compared to their short-term evolving counterparts under identical conditions.