Phase transition in the controllability of temporal networks

Márton Pósfai, Philipp Hövel

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 complex systems for which the timescale of the dynamics we control and the timescale of changes in the network are comparable. We provide both 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, present analytical results for a generic class of temporal network models, and preform measurements using data collected from a real system. Depending upon the density of the interactions compared to the timescale of the dynamics, we witness a phase transition describing the sudden emergence of a giant controllable subspace spanning a finite fraction of the network. We also study the role of temporal patterns and network topology in real data making use of various randomization procedures, finding that the overall activity and the degree distribution of the underlying network are the main features influencing controllability.

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