  We focus on non-consensus opinion models in which above a certain threshold
two opinions coexist in a stable relationship. We revisit and extend the
non-consensus opinion (NCO) model introduced by Shao. We generalize the NCO
model by adding a weight factor W to individual's own opinion when determining
its future opinion (NCOW model). We find that as W increases the minority
opinion holders tend to form stable clusters with a smaller initial minority
fraction compared to the NCO model. We also revisit another non-consensus
opinion, the inflexible contrarian opinion (ICO) model, which introduces
inflexible contrarians to model a competition between two opinions in the
steady state. In the ICO model, the inflexible contrarians effectively decrease
the size of the largest cluster of the rival opinion. All of the above models
have previously been explored in terms of a single network. However opinions
propagate not only within single networks but also between networks, we study
here the opinion dynamics in coupled networks. We apply the NCO rule on each
individual network and the global majority rule on interdependent pairs. We
find that the interdependent links effectively force the system from a second
order phase transition, which is characteristic of the NCO model on a single
network, to a hybrid phase transition, i.e., a mix of second-order and abrupt
jump-like transitions that ultimately becomes, as we increase the percentage of
interdependent agents, a pure abrupt transition. We conclude that for the NCO
model on coupled networks, interactions through interdependent links could push
the non-consensus opinion type model to a consensus opinion type model, which
mimics the reality that increased mass communication causes people to hold
opinions that are increasingly similar.
