Abstract
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.
Highlights
Complex systems consist of many interacting elements, and the web of these interactions is best described as a complex network
We provide analytical and computational tools to study controllability based on temporal network characteristics
We provide an analytical solution for a simple class of model networks to gain insight on the effect of the degree distribution and the choice of Δt
Summary
Complex systems consist of many interacting elements, and the web of these interactions is best described as a complex network. Recent work by Liu et al spurred interest in network control [9] They found that, if the system can be represented by a directed weighted network, assuming linear dynamics and invoking the framework of structured systems [10, 11], it is possible to study control-related questions by only using information about the underlying network. This enabled the research community to apply the full arsenal of network science to the problem, uncovering various nontrivial phenomena emerging from the complexity of the structure of the system [12,13,14,15,16,17]. One must include the temporal aspect of the interactions when studying the controllability of networks with timevarying topologies
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