  Much recent research on social networks has focused on the modeling and
analysis of how opinions evolve as a function of interpersonal relationships.
It is also of great interest to model and understand the implications of
friendly and antagonistic relationships. In this paper, we propose a new,
simple and intuitive model that incorporates the socio-psychological phenomenon
of the boomerang effect in opinion dynamics. We establish that, under certain
conditions on the structure of the signed network that corresponds to the
so-called structural balance property, the opinions in the network polarize.
Compared to other models in the literature, our model displays a richer and
perhaps more intuitive behavior of the opinions when the social network does
not satisfy structural balance. In particular, we analyze signed networks in
which the opinions show persistent fluctuations (including the case of the
so-called clustering balance).
