Signed Friedkin–Johnsen Models: Opinion Dynamics With Stubbornness and Antagonism

The aim of this article is to investigate how opinions propagate in presence of stubborn behavior (i.e., agents that tend to defend their stance) and of signed (i.e., antagonistic) interactions among the agents. The stability properties of the resulting system, denoted signed Friedkin–Johnsen (SFJ) model, are studied in detail, and also the convergence to consensus for a concatenation of such SFJ models. A noteworthy feature of the SFJ model is that the opinion dynamics need not be confined to the convex hull of the initial conditions, meaning that cleavage can increase because of the antagonistic interactions. In particular, we show that the concatenated SFJ model can behave as a nonnormal system, in which the opinions transiently distance themselves only to rejoin a common consensus value asymptotically.