Eur. Phys. J. Special Topics 224, 3325-3342 (2015)
https://doi.org/10.1140/epjst/e2015-50087-9

Regular Article

On the control of the Heider balance model*

¹ Institut für Mathematik, Universität Würzburg, Emil-Fischer-Strasse 31, 97074 Würzburg, Germany
² Conservatoire National des Arts et Métiers, Équipe M2N, 292 rue Saint-Martin, 75003 Paris, France
³ Faculty of Physics and Applied Computer Science, AGH University of Science and Technology al. Mickiewicza 30, 30059 Krakòw, Poland
⁴ Institut für Mathematik, Universität Würzburg, Emil-Fischer-Strasse 30, 97074 Würzburg, Germany

^a e-mail: suttida.wongkaew@mathematik.uni-wuerzburg.de
^b e-mail: marco.caponigro@cnam.fr
^c e-mail: kulakowski@novell.ftj.agh.edu.pl
^d e-mail: alfio.borzi@mathematik.uni-wuerzburg.de

Received: 16 April 2015
Revised: 2 November 2015
Published online: 15 December 2015

Abstract

The Heider social balance model describes the evolution of the relationships in a social network of humans or animals. This model is built upon the concept of balance of triads consisting of friendly or hostile edges representing the state of the network. In this differential model, a leader is introduced in order to control the system and to drive the social network to a desired relationship state. Further, the stability, the local controllability, and the optimal control through leadership of the Heider model are investigated. Results of numerical experiments demonstrate the ability of the proposed control strategy to drive the Heider balance model to friendship.