Control Principles of Complex Networks

TL;DR

This paper reviews recent advances in understanding how the structure and dynamics of complex networks influence their controllability, aiming to uncover fundamental control principles of complex systems.

Contribution

It synthesizes mathematical results, empirical findings, and applications to elucidate the control principles governing complex networks.

Findings

Network topology critically influences controllability.

Control principles reveal how structure and dynamics interact.

Understanding control can inform the design of better complex systems.

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 nonlinear dynamics 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 here we review recent advances on the controllability and the control of complex networks, exploring the intricate interplay between a system's structure, captured by its network topology, and the dynamical laws that govern the interactions between the components. We match the pertinent mathematical results with empirical findings and applications. We show that uncovering the control principles of complex systems can help us explore and ultimately understand the fundamental laws that govern their behavior.