  Understanding how opinions spread through a community or how consensus
emerges in noisy environments can have a significant impact on our
comprehension of social relations among individuals. In this work a model for
the dynamics of opinion formation is introduced. The model is based on a
nonlinear interaction between opinion vectors of agents plus a stochastic
variable to account for the effect of noise in the way the agents communicate.
The dynamics presented is able to generate rich dynamical patterns of
interacting groups or clusters of agents with the same opinion without a leader
or centralized control. Our results show that by increasing the intensity of
noise, the system goes from consensus to a disordered state. Depending on the
number of competing opinions and the details of the network of interactions,
the system displays a first- or a second-order transition. We compare the
behavior of different topologies of interactions: one-dimensional chains, and
annealed and complex networks.
