Abstract
Complex systems are omnipresent and play a vital role in in our every-day lives. Adverse behavior of such systems has generated considerable interest in being able to control complex systems modeled as networks. Here, we propose a topology-dynamics-based approach for controlling complex systems modeled as networks of coupled multi-dimensional dynamical entities. For given dynamics and topology, we introduce an efficient scheme to identify in polynomial time a finite set of driver nodes, which – when endowed with the control function – steer the network to the desired behavior. We demonstrate the high suitability of our approach by controlling various networked multi-dimensional dynamics, coupled onto different topologies.
Highlights
Complex systems are omnipresent and play a vital role in in our every-day lives
We note though that one can employ our approach in cases where the desired state is a nominal trajectory by combining it with the master stability function (MSF) formalism[26,27] (Supplementary Information)
Applying our control strategy to the system presented in the upper part of Fig. 1, we find that only ND = 10 driver nodes are required to steer the system dynamics from the undesired state to the desired one
Summary
Complex systems are omnipresent and play a vital role in in our every-day lives. Adverse behavior of such systems has generated considerable interest in being able to control complex systems modeled as networks. Control through adjustments of the initial condition of the dynamics (placing the system in a new basin of attraction)[21], control through change of parameters and exploiting network regulatory attributes[22] and controlling chaos[23] are known works conducted in this category. Another strategy developed recently in this category, based on the concepts of “feedback vertex set” and “determining nodes”, is the so called “feedback vertex control”[24,25] which is almost independent of the underlying dynamics of the network and mostly depends on the wiring of the system and knowledge of the target invariant sets
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