Heider Balance-A Continuous Dynamics

Abstract

This paper is a short review on applications of non-linear dynamics in the concept of Heider balance, known also as structural balance. In all the papers listed here, the basic tools are ordinary differential equations. All papers pay attention to real social phenomena, which play the role of illustrations of the mathematical formalisms.

Keywords: cognitive dissonance; differential equations; social simulations.

Figure 1

Four possible states of a triad of links, where blue continuous lines mean positive (friendly) relations, and red dashed lines mean negative (hostile) relations. The product of three relations within a triad is positive for balanced triads, as in (a,b), and negative for imbalanced triads, as in (c,d).

Figure 2

The generic scheme of asymmetric relations between four communities [26]. Continuous lines mean friendly relations, and dashed lines are hostile ones. Relations to members of the same community are marked by curvy lines, continuous for $N_1$ and $N_2$, and dashed for $N_3$ and $N_4$.