Social dynamics with peer support on heterogeneous networks: The "mafia model"

Human behavior often exhibit a scheme in which individuals adopt
indifferent, neutral, or radical positions on a given topic. The
mechanisms leading to community formation are strongly related with
social pressure and the topology of the contact network. Here, we
discuss an approach to model social behavior which accounts for the
protection by alike peers proportional to their relative abundance
in the closest neighborhood. We explore the ensuing non-linear
dynamics emphasizing the role of the specific structure of the
social network, modeled by scale-free graphs. We find that both
coexistence of opinions and consensus on the default position are
possible stationary states of the model. In particular, we show how
these states critically depend on the heterogeneity of the social
network and the specific distribution of external control elements.