Structural controllability of temporal networks

The control of complex systems is an ongoing challenge of complexity research. Recent advances using concepts of structural control deduce a wide range of control related properties from the network representation of complex systems. Here, we examine the controllability of systems for which the timescale of the dynamics we control and the timescale of changes in the network are comparable. We provide analytical and computational tools to study controllability based on temporal network characteristics. We apply these results to investigate the controllable subnetwork using a single input. For a generic class of model networks, we witness a phase transition depending upon the density of the interactions, describing the emergence of a giant controllable subspace. We show the existence of the two phases in real-world networks. Using randomization procedures, we find that the overall activity and the degree distribution of the underlying network are the main features influencing controllability.