Emergence of complexity in controlling simple regular networks
School of Systems Science, Beijing Normal University - Beijing, 100875, PRC
Received: 29 February 2016
Accepted: 20 June 2016
Quantifying the capacity of a given node or a bunch of nodes in maintaining a system's controllability is a crucial problem in complex networks and control theory. We give a systematic analysis of the ability of a single node or a pairs of nodes to control an undirected unweighted chain and ring. By combining algebraic theory and graph spectrum analysis, we derive analytic expressions for the control range of some given control inputs and find that complex phenomena emerge even from these simplest graph structures. Specifically, the control range is sensitive to the location of driver nodes and shows complex periodic behaviors. Our findings have implications for evaluating the control range and practically controlling complex networks.
PACS: 89.75.-k – Complex systems / 02.30.Yy – Control theory / 02.10.Ud – Linear algebra
© EPLA, 2016