Synchronization phenomena in a higher-order neuronal network with random blinking in the functional forms of the coupling

In this article, we investigate synchronization phenomena in a network of chaotic Hindmarsh–Rose neurons involving pairwise and three-body interactions that alter over time. The frozen structure of the network is encoded by a two-dimensional simplicial complex and the involved components of the functional forms of the coupling switch on and off at random and repeatedly over time. The complete chaotic synchronization of the networked neurons is investigated by the master stability function approach which reveals that, in the case of fast blinking, an appropriate combination of the different blinking components of the coupling functions improves the ability of the neurons to oscillate in synchrony, compared to frozen single-variable coupling schemes. In addition, we find that for appropriately chosen coupling blinking probabilities, this random blinking coupling scenario outperforms the regular blinking coupling scheme considered in the previous works. An increase in the minimal blinking time period induces the progressive impairment of the synchronizability of the time-varying neuronal network which is expressed by the shrinkage of the stability range of the synchronized state, as well as the onset of intermittent synchronization in an increasingly larger coupling parameter region at the transition from completely synchronized to completely desynchronized dynamics. On the other hand, leveraging the symmetry property of the adjacency tensor of three-body interactions, we show that the higher-order network structure is equivalent to the corresponding classical graph where the effective coupling strength is a linear combination of the strengths of pairwise and three-body interactions. The examination of this reduced network model helps explaining the scaling of the completely and intermittent synchronized patterns to lower coupling strengths when three-body interactions are incorporated to the coupling.