Abstract
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.
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