Assortativity-induced explosive synchronization in a complex neuronal network

In this study, we consider a scale-free network of nonidentical Chialvo neurons, coupled through electrical synapses. For sufficiently strong coupling, the system undergoes a transition from completely out of phase synchronized to phase synchronized state. The principal focus of this study is to investigate the effect of the degree of assortativity over the synchronization transition process. It is observed that, depending on assortativity, bistability between two asymptotically stable states allows one to develop a hysteresis loop which transforms the phase transition from second order to first order. An expansion in the area of hysteresis loop is noticeable with increasing degree-degree correlation in the network. Our study also reveals that effective frequencies of nodes simultaneously go through a continuous or sudden transition to the synchronized state with the corresponding phases. Further, we examine the robustness of the results under the effect of network size and average degree, as well as diverse frequency setup. Finally, we investigate the dynamical mechanism in the process of generating explosive synchronization. We observe a significant impact of lower degree nodes behind such phenomena: in a positive assortative network the low degree nodes delay the synchronization transition.

Automated summary

This study investigates the synchronization transition process in a scale-free network of nonidentical Chialvo neurons, focusing on the effect of the degree of assortativity. The research reveals that assortativity can lead to bistability between asymptotically stable states and transform the phase transition from second order to first order, with an expansion in the hysteresis loop area. Additionally, the study examines the simultaneous transitions of node frequencies to the synchronized state with phases and the impact of lower degree nodes on synchronization transition in positive assortative networks.