Abstract
In pinning control of complex networks, it is assumed that, with the same pinning effort, the network dynamics is better controlled by pinning the large-degree nodes than by pinning the small-degree ones. Here, by varying the number of pinned nodes, we find that, when a significant fraction of the nodes are pinned in a complex network, the pinning of the small-degree nodes will generally give a higher performance than that of the large-degree ones. We demonstrate this interesting phenomenon on a variety of complex networks, and analyze its underlying mechanisms through the simple model of strongly pinned star-structure network. By changing the network topological properties, we also find that the advantage of the small-degree pinning strategy is more distinct in sparsely connected heterogeneous networks than in densely connected homogeneous networks. The findings are believed to be beneficial for the design of control schemes in some practical systems, as well as to shed new light on the dynamics of complex networks.