Control Principles of Complex Systems

Y.-Y. Liu, A.-L. Barabasi.
Review of Modern Physics
88:3, 035006-035064 (2016).
September 6, 2016

Abstract

A reflection of our  ultimate understanding of a complex system is our ability to control its  behavior. Typically, control has multiple prerequisites: it requires an  accurate map of the network that governs the interactions between the  system's components, a quantitative description of the dynamical laws that  govern the temporal behavior of each component, and an ability to influence  the state and temporal behavior of a selected subset of the components. With  deep roots in dynamical systems and control theory, notions of control and  controllability have taken a new life recently in the study of complex  networks, inspiring several fundamental questions: What are the control  principles of complex systems? How do networks organize themselves to balance  control with functionality? To address these questions here recent advances  on the controllability and the control of complex networks are reviewed,  exploring the intricate interplay between the network topology and dynamical  laws. The pertinent mathematical results are matched with empirical findings  and applications. Uncovering the control principles of complex systems can  help us explore and ultimately understand the fundamental laws that govern  their behavior.