Effect of network architecture on burst and spike synchronization in a scale-free network of bursting neurons

• A directed scale-free network of bursting neurons is considered.
• Effect of network architecture on burst and spike synchronization is investigated.
• Average path length and betweenness centralization affect the synchronization.
• In-degree distribution also affects the synchronization.

We investigate the effect of network architecture on burst and spike synchronization in a directed scale-free network (SFN) of bursting neurons, evolved via two independent αα- and ββ-processes. The αα-process corresponds to a directed version of the Barabási–Albert SFN model with growth and preferential attachment, while for the ββ-process only preferential attachments between pre-existing nodes are made without addition of new nodes. We first consider the “pure” αα-process of symmetric preferential attachment (with the same in- and out-degrees), and study emergence of burst and spike synchronization by varying the coupling strength JJ and the noise intensity DD for a fixed attachment degree. Characterizations of burst and spike synchronization are also made by employing realistic order parameters and statistical-mechanical measures. Next, we choose appropriate values of JJ and DD where only burst synchronization occurs, and investigate the effect of the scale-free connectivity on the burst synchronization by varying (1) the symmetric attachment degree and (2) the asymmetry parameter (representing deviation from the symmetric case) in the αα-process, and (3) the occurrence probability of the ββ-process. In all these three cases, changes in the type and the degree of population synchronization are studied in connection with the network topology such as the degree distribution, the average path length LpLp, and the betweenness centralization BcBc. It is thus found that just taking into consideration LpLp and BcBc (affecting global communication between nodes) is not sufficient to understand emergence of population synchronization in SFNs, but in addition to them, the in-degree distribution (affecting individual dynamics) must also be considered to fully understand for the effective population synchronization.