Aperiodic dynamics in a deterministic adaptive network model of attitude formation in social groups

Adaptive network models, in which node states and network topology coevolve, arise naturally in models of social dynamics that incorporate homophily and social influence. Homophily relates the similarity between pairs of nodes’ states to their network coupling strength, whilst social influence causes coupled nodes’ states to convergence. In this paper we propose a deterministic adaptive network model of attitude formation in social groups that includes these effects, and in which the attitudinal dynamics are represented by an activator-inhibitor process. We illustrate that consensus, corresponding to all nodes adopting the same attitudinal state and being fully connected, may destabilise via Turing instability, giving rise to aperiodic dynamics with sensitive dependence on initial conditions. These aperiodic dynamics correspond to the formation and dissolution of sub-groups that adopt contrasting attitudes. We discuss our findings in the context of cultural polarisation phenomena.