Three-state opinion dynamics in modular networks.

In this work we study the opinion evolution in a community-based population with intergroup interactions. We address two issues. First, we consider that such intergroup interactions can be negative with some probability p. We develop a coupled mean-field approximation that still preserves the community structure and it is able to capture the richness of the results arising from our Monte Carlo simulations: continuous and discontinuous order-disorder transitions as well as nonmonotonic ordering for an intermediate community strength. In the second part, we consider only positive interactions but with the presence of inflexible agents holding a minority opinion. We also consider an indecision noise: a probability q that allows the spontaneous change of opinions to the neutral state. Our results show that the modular structure leads to a nonmonotonic global ordering as q increases. This inclination toward neutrality plays a dual role: A moderated propensity to neutrality helps the initial minority to become a majority, but this noise-driven opinion switching becomes less pronounced if the agents are too susceptible to become neutral.