Energy cost study for controlling complex social networks with conformity behavior

TL;DR

This paper investigates the energy required to control complex social networks exhibiting conformity behavior, using discrete-time models, and finds that conformity reduces control energy needs, with implications for social systems like flocking and evolutionary games.

Contribution

It introduces a discrete-time modeling approach for controlling social networks with conformity, deriving new energy cost scaling laws and validating them on real and model networks.

Findings

Controlling networks with conformity requires less energy.

Heterogeneous scale-free networks are less controllable.

Conformity influences control energy and network controllability.

Abstract

In order to understand controlling a complex system, an estimation of the required effort needed to achieve control is vital. Previous works have addressed this issue by studying the scaling laws of energy cost in a general way with continuous-time linear dynamics. However, continuous-time linear dynamics is unable to capture conformity behavior, which is common in many complex social systems. Therefore, to understand controlling social systems with conformity, discrete-time modelling is used and the energy cost scaling laws are derived. The results are validated numerically with model and real networks. In addition, the energy costs needed for controlling systems with and without conformity are compared, and it was found that controlling networked systems with conformity features always requires less control energy. Finally, it is shown through simulations that heterogeneous scale-free networks are less controllable, requiring a higher number of minimum drivers. Since the conformity-based model relates to various complex systems, such as flocking, or evolutionary games, the results of this paper represent a step forward towards developing realistic control of complex social systems.