Effects of noise on synchronization in simplicial complexes

Abstract This paper explores the synchronization of stochastic simplicial complexes with noise, modeled by stochastic differential equations of Itô type. It establishes the relationship between synchronization and individual dynamics, higher-order structures, coupling strengths, and noise. In particular, this study delves into the role of multi-body interactions, particularly focusing on the influence of higher-order simplicial structures on the overall synchronization behavior. Furthermore, the effects of noise on synchronizability in the stochastic simplicial complex are thoroughly examined. The obtained results indicate that the effects of noise on the synchronizability vary with the manner in which noise propagates. The presence of noise can regulate the synchronization pattern of the simplicial complex, transforming the unstable state into a stable state, and vice versa. These findings offer valuable insights and a theoretical foundation for improving the performance of real-world networks, such as communication networks, biological systems, and social networks, where noise is often inevitable.