Neuronal synchronization in time-varying higher-order networks.

A potential issue of interest is figuring out how the combination of temporal and higher-order interactions influences the collective dynamics of the brain, specifically, neuronal synchronization. Motivated by this, here we consider an ensemble of neurons interacting with each other through gap junctions, modeled by temporal higher-order networks (simplicial complexes), and study the emergence of complete neuronal synchronization. We find that the critical synaptic strength for achieving neuronal synchronization with time-varying higher-order interaction is relatively lower than that with temporal pairwise interactions or static many-body interactions. Our study shows that neuronal synchronization can occur even in the sole presence of higher-order, time-varying interactions. We also find that the enhancement in neuronal synchronization in temporal higher-order structure is highly related to the density of group interactions among the neurons. Furthermore, to characterize the local stability of the synchronous solution, we use the master stability function approach, which shows that the numerical findings are in good agreement with the analytically derived conditions.