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

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 alpha- and beta-processes. The alpha-process corresponds to a directed version of the Barabasi-Albert SFN model with growth and preferential attachment, while for the beta-process only preferential attachments between pre-existing nodes are made without addition of new nodes. We first consider the pure'' alpha-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 J and the noise intensity D 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 J and D 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 alpha-process, and (3) the occurrence probability of the beta-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 L-p, and the betweenness centralization B-c. It is thus found that just taking into consideration L-p and B-c (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. (C) 2016 Elsevier Ltd. All rights reserved.