  Homophily and social influence are the fundamental mechanisms that drive the
evolution of attitudes, beliefs and behaviour within social groups. Homophily
relates the similarity between pairs of individuals' attitudinal states to
their frequency of interaction, and hence structural tie strength, while social
influence causes the convergence of individuals' states during interaction.
Building on these basic elements, we propose a new mathematical modelling
framework to describe the evolution of attitudes within a group of interacting
agents. Specifically, our model describes sub-conscious attitudes that have an
activator-inhibitor relationship. We consider a homogeneous population using a
deterministic, continuous-time dynamical system. Surprisingly, the combined
effects of homophily and social influence do not necessarily lead to group
consensus or global monoculture. We observe that sub-group formation and
polarisation-like effects may be transient, the long-time dynamics being
quasi-periodic with sensitive dependence to initial conditions. This is due to
the interplay between the evolving interaction network and Turing instability
associated with the attitudinal state dynamics.
