We investigate the effect of network architecture on burst and spikesynchronization 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 Barab\'{a}si-AlbertSFN model with growth and preferential attachment, while for the$\beta-$process only preferential attachments between pre-existing nodes aremade without addition of new nodes. We first consider the "pure"$\alpha-$process of symmetric preferential attachment (with the same in- andout-degrees), and study emergence of burst and spike synchronization by varyingthe coupling strength $J$ and the noise intensity $D$ for a fixed attachmentdegree. Characterizations of burst and spike synchronization are also made byemploying realistic order parameters and statistical-mechanical measures. Next,we choose appropriate values of $J$ and $D$ where only the burstsynchronization occurs, and investigate the effect of the scale-freeconnectivity on the burst synchronization by varying (1) the symmetricattachment degree and (2) the asymmetry parameter (representing deviation fromthe symmetric case) in the $\alpha-$process, and (3) the occurrence probabilityof the $\beta-$process. In all these three cases, changes in the type and thedegree of population synchronization are studied in connection with the networktopology such as the degree distribution, the average path length $L_p$, andthe betweenness centralization $B_c$. It is thus found that not only $L_p$ and$B_c$ (affecting global communication between nodes) but also the in-degreedistribution (affecting individual dynamics) are important network factors foreffective population synchronization in SFNs.
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