Optimal pinning synchronization on directed complex network.

In this paper, pinning synchronization on directed network was considered. By analyzing, some general synchronization criteria on directed network were established. And then, we verified it on directed globally coupled network, directed scale-free network, and directed small-world network, respectively. The pinning nodes were selected, respectively, according to order of in-degrees and out-degrees. Through comparing and analyzing simulations, the optimal pinning scheme was found, and a practical principle was induced finally.