Synchronization in a higher-order neuronal network with blinking interactions

Abstract

The synchronization of higher-order networks presents a fascinating area of exploration within nonlinear dynamics and complex networks. Simultaneously, growing research interest focuses on uncovering synchronization dynamics in time-varying networks with time-dependent coupling structures, reflecting their prevalence in real-world systems like neuronal networks. Motivated by this, the present study delves into the synchronization phenomenon within a higher-order network incorporating a blinking coupling scheme. Blinking coupling is an on–off switching coupling that has been demonstrated to enhance synchronization effectively. Its efficacy stems from ensuring synchronization, as the master stability function (MSF) follows a linear pattern. In this study, our objective is to investigate such a time-varying coupling scheme in a higher-order network configuration. We investigate the influence of coupling parameters and blinking frequency on synchronization behavior. Notably, our findings demonstrate that as the blinking frequency increases, the network exhibits a gradual convergence toward the behavior of the average network. Furthermore, leveraging the analytical framework of MSF and the average synchronization error, we provide analytical and numerical evidence confirming that the MSF pattern within the average network transforms into a linear function. The synchronous and asynchronous regions also exhibit a clear separation demarcated by a linear curve across the coupling parameter space. Moreover, our results suggest that incorporating higher-order interactions fosters enhanced synchrony by effectively scaling the synchronization patterns to lower coupling parameter values.