The evolution of interpersonal relationships to structural balance involves various complex social psychological mechanics, including interpersonal influences, opinion dynamics, person-person homophily, person-entity homophily, etc. In this paper, we propose a discrete-time nonlinear dynamical system that characterizes the complex interplay among all the above mechanisms. Specifically, interpersonal appraisals are updated based on person-person homophily and person-opinion homophily; the social influence matrix is built according to the interpersonal appraisals; and the opinion dynamics evolve on the social influence network. Via theoretical analysis, we characterize the finite-time behavior and the equilibrium set of the model. In addition, we establish the equivalence among social balance, modulus consensus, convergence, and the non-vanishing appraisal condition. Moreover, we provide sufficient conditions such that the current faction formation in social balance is changed by introducing additional opinion dimensions, i.e., by setting new agendas. Numerical examples show the effectiveness of such agenda-setting strategy and indicate that sufficiently extreme topics are required in order to successfully conduct such manipulation. (c) 2024 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Publication:

Automatica Volume 167, September 2024

https://doi.org/10.1016/j.automatica.2024.111797

Author:

Fangzhou Liu

National Key Laboratory of Modeling and Simulation for Complex Systems, Harbin Institute of Technology, 150001 Harbin, China

Email：fangzhou.liu@hit.edu.cn

Shaoxuan Cui

Bernoulli Institute, Faculty of Science and Engineering, University of Groningen, The Netherlands

Email：s.cui@rug.nl

Ge Chen

Key Laboratory of Systems and Control Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China

Email：chenge@amss.ac.cn

Wenjun Mei

Department of Mechanics and Engineering Science, Peking University, China

Email：mei@pku.edu.cn

Huijun Gao

Research Institute of Intelligent Control and Systems, School of Astronautics, Harbin Institute of Technology, China

Email：hjgao@hit.edu.cn