Controlling complex networks with conformity behavior

¹ School of Electrical & Electronic Engineering, East China Jaotong University - Nanchang, Jiangxi 330013, PRC
² Department of Modern Physics, University of Science and Technology of China - Hefei, Anhui 230026, PRC
³ School of Systems Science, Beijing Normal University - Beijing 100875, PRC
⁴ School of Electrical, Computer and Energy Engineering, Arizona State University - Tempe, AZ 85287, USA
⁵ College of Physics and Electronic Information Engineering, Wenzhou University - Wenzhou, Zhejiang 325035, PRC
⁶ School of Science, Southwest University of Science and Technology - Mianyang, Sichuan 621010, PRC

^(a) wenxuwang@bnu.edu.cn
^(b) bhwang@ustc.edu.cn

Received: 25 April 2015
Accepted: 14 September 2015

Abstract

Controlling complex networks accompanied by common conformity behavior is a fundamental problem in social and physical science. Conformity behavior that individuals tend to follow the majority in their neighborhood is common in human society and animal communities. Despite recent progress in understanding controllability of complex networks, the existent controllability theories cannot be directly applied to networks associated with conformity. Here we propose a simple model to incorporate conformity-based decision making into the evolution of a network system, which allows us to employ the exact controllability theory to explore the controllability of such systems. We offer rigorous theoretical results of controllability for representative regular networks. We also explore real networks in different fields and some typical model networks, finding some interesting results that are different from the predictions of structural and exact controllability theory in the absence of conformity. We finally present an example of steering a real social network to some target states to further validate our controllability theory and tools. Our work offers a more realistic understanding of network controllability with conformity behavior and can have potential applications in networked evolutionary games, opinion dynamics and many other complex networked systems.