Complete synchronization in Hindmarsh–Rose neuronal networks through the interplay of electrical and chemical synaptic higher-order interactions

We investigate the collective dynamics of neuronal networks incorporating both electrical and chemical higher-order interactions (HOIs). Unlike traditional pairwise coupling models, electrical triadic and chemical synaptic HOIs introduce nonlinear effects that profoundly influence network behavior. Using a network of Hindmarsh–Rose neurons, we first analyze a regular network where the interplay between pairwise and triadic electrical couplings leads to a clear transition from incoherent to completely synchronized states. To characterize these dynamical regimes, we employ the synchronization error (SE) and mean amplitude range (MAR) as quantitative measures. We find that electrical HOIs accelerate synchronization and broaden the parameter region supporting coherent oscillations, while chemical HOIs induce nontrivial amplitude death, stabilizing uniform nonzero steady states absent in purely electrical networks. Extending the analysis to small-world and random topologies shows that these effects persist across network structures, with increasing randomness further enlarging the synchronization domain. Using the master stability function approach, we validate that pairwise and triadic electrical interactions govern the onset of complete synchronization. Our results highlight how electrical and chemical HOIs jointly enhance synchronization, providing new insights into the mechanisms underlying coordinated activity in complex neuronal systems.