ABSTRACT This paper investigates the stability of synchronous states in multilayer nonlinear complex networks incorporating simplicial complexes. We employ the connection graph method and extend it to high‐order networks to examine the relationship between synchronization behavior and network structure. Additionally, we derive a formula for the coupling strength required for the system to achieve synchronization. Furthermore, we consider time‐varying networks and analyze the relationship between the synchronization threshold, connection probability, and switching frequency. Numerical results demonstrate that the predicted coupling strength aligns with the actual required coupling strength. We also find that the number of simplicial complexes has a dominant influence on synchronization. Moreover, the results indicate that when the load on a particular edge becomes excessive (such that reusing the edge leads to failure), the coupling strength required for synchronization increases. Our findings suggest that in real complex networks, high‐order interactions can significantly enhance network stability under an average distribution; however, when high‐order interaction forces aggregate, the improvement in stability is limited.
Guo et al. (Wed,) studied this question.