Realistic control of network dynamics

Abstract

The control of complex networks is of paramount importance in areas as diverse as ecosystem management, emergency response, and cell reprogramming. A fundamental property of networks is that perturbations to one node can affect other nodes, potentially causing the entire system to change behavior or fail. Here, we show that it is possible to exploit the same principle to control network behavior. Our approach accounts for the nonlinear dynamics inherent to real systems, and allows bringing the system to a desired target state even when this state is not directly accessible due to constraints that limit the allowed interventions. Applications show that this framework permits reprogramming a network to a desired task as well as rescuing networks from the brink of failure—which we illustrate through the mitigation of cascading failures in a power-grid network and the identification of potential drug targets in a signaling network of human cancer.

Control principles of complex systems

“…We need, therefore, tools to bring a networked system to a desired target state. A recently proposed method can work even when the target state is not directly accessible due to certain constraints (Cornelius et al, 2013). The basic insight of the approach is that each desirable state has a "basin of attraction", representing a region of initial conditions whose trajectories converge to it.…”

“…V.A.1, the approach based on compensatory perturbation potentially works for any nonlinear system. It has been successfully applied to the mitigation of cascading failures in a power grid and the identification of drug targets in a cancer signaling network (Cornelius et al, 2013). Yet, the approach requires a priori knowledge of the detailed model describing the dynamics of the system we wish to control, a piece of knowledge we often lack in complex systems.…”

“…(b) Systematic design of compensatory perturbations of state variables that take advantage of the full basin of attraction of the desired final state (Cornelius et al, 2013). (c) Construction of the attractor network (Lai, 2014;Wang et al, 2014); (d) Mapping the control problem into a combinatorial optimization problem on the underlying networks Mochizuki et al, 2013).…”

“…Consequently, the traditional theory of complex systems has predominantly focused on the measurement and the modeling problem. Recently, however, questions pertaining to the control of complex networks became an important research topic in statistical physics (Cornelius et al, 2013;Liu et al, 2011a;Nepusz and Vicsek, 2012;Ruths and Ruths, 2014;Sun and Motter, 2013;Yan et al, 2012). This interest is driven by the challenge to understand the fundamental control principles of an arbitrary self-organized system.…”

On controlling networks of limit-cycle oscillators

“…For instance, the concept of controllability of complex networks has been established using control theory for linear dynamical systems [14][15][16][17][18] . Significant advances have also been made in the control of several a) Electronic mail: persebastian.skardal@trincoll.edu nonlinear networks-connected dynamical systems [19][20][21][22][23] . A particularly important family of network-coupled nonlinear dynamical systems that plays an important role in modeling phenomena ranging from synchronization of power grids 24 to cardiac excitation 25 are networks of coupled oscillators 26 .…”