Explosive synchronization and hysteresis in FitzHugh–Nagumo neural networks with higher-order interactions

Abstract This study investigates the impact of higher-order interactions on explosive synchronization and hysteresis in FitzHugh–Nagumo neural networks. We construct a higher-order network model incorporating pairwise (1-simplex) and three-body (2-simplex) interactions, along with a nonlinear coupling mechanism inspired by the Rosenzweig-MacArthur model. Using the order parameter and standard deviation as metrics, we analyze synchronization dynamics through numerical simulations. Our results demonstrate that higher-order interactions not only enhance the explosive synchronization but also induce hysteresis, with the hysteresis width growing as higher-order coupling strengthens. Furthermore, increasing noise intensity suppresses the bistability induced by higher-order interactions, ultimately eliminating hysteresis. These findings reveal the critical role of higher-order interactions in synchronization dynamics, offering theoretical insights for controlling collective behavior in neuroscience, ecology, and related fields. This work advances the understanding of synchronization in complex systems and provides new methodologies for studying multi-body interactions in real-world networks.