Title: Steering opinion dynamics through controlling the underlying network
Abstract: The field of opinion dynamics has recently seen a large interest in the mathematics community, both from modelling and control perspectives. Most works focus on the Hegselmann-Krause model, a widely used bounded confidence model, and typical control strategies aim to steer a system towards consensus (or make it so more quickly) by using controls that act directly on agents. In this talk, I will propose a novel type of control based on adaptive networks: I will introduce recent work on co-evolving networks (i.e. a dynamical system where the underlying network evolves at the same time as, and influenced by, the individuals’ opinions) and how to control the network system in such a way that the opinion dynamics moves to consensus or other desired states. I will present various control strategies and analyse under which conditions opinions can or cannot be steered towards a given target, then corroborate and extend our analytical results with computational experiments and a study of optimal controls. I will highlight the advantages and disadvantages of each approach, as well as propose several directions for future research. If time permits, I will also discuss recent work on introducing ageing effects, which allows us to explore the mean-field limit and long time behaviour of these models, beyond just reaching consensus.