Effects of network structure on the synchronizability of nonlinearly coupled Hindmarsh–Rose neurons

• We investigate the effects of network structure on the synchronizability of nonlinearly coupled Hindmarsh–Rose neurons.
• We mainly consider the networks that exhibit the small-world character or scale-free property.
• The synchronizability of three specific network ensembles with prescribed network structures are compared.
• Networks with more connections will not necessarily result in better synchronizability.

This work is devoted to investigate the effects of network structure on the synchronizability of nonlinearly coupled dynamical network of Hindmarsh–Rose neurons with a sigmoidal coupling function. We mainly focus on the networks that exhibit the small-world character or scale-free property. By checking the first nonzero eigenvalue of the outer-coupling matrix, which is closely related to the synchronization threshold, the synchronizabilities of three specific network ensembles with prescribed network structures are compared. Interestingly, we find that networks with more connections will not necessarily result in better synchronizability.