Delay-induced synchronization transitions in modular scale-free neuronal networks with hybrid electrical and chemical synapses

•Time delay can induce synchronization transitions in modular neuronal networks.•The transition is more profound for larger probability of electrical synapses.•Modular network parameters can also induce transitions to burst synchronization.•Two types of synapse can perform different but complementary synchronization roles.

We study the dependence of synchronization transitions in modular networks of bursting neurons with hybrid electrical–chemical synapses on the information transmission delay and the probability of electrical synapses. The modular network is composed of subnetworks (clusters); each of them presents the scale-free property. It is shown that, irrespective of the probability of electrical synapses, the time delay can always induce synchronization transitions in modular neuronal networks. Regions of synchronization and non-synchronization appear intermittently as the delay increases. In particular, all these transitions to burst synchronization occur approximately at integer multiples of oscillatory period of individual neurons. In addition, for larger probability of electrical synapses, the intermittent synchronization transition is more profound, due to the stronger synchronization capability of electrical synapses compared with chemical ones. Furthermore, the transition to synchronous bursting can also be induced by the variation of modular network parameters, that is, the coupling strength between neurons, the interconnection probability between different subnetworks, as well as the number of subnetworks. Particularly, we find that a modular neuronal network is harder to get global synchronization when constituting neurons are dispersed over more clusters. On the other hand, chemical and electrical synapses can perform complementary roles in the synchronization of hybrid modular neuronal networks: the larger the electrical synapse strength is the smaller the chemical synapse strength needed to achieve burst synchronization.