  In this work we propose and investigate a strategy to prevent consensus in
kinetic models for opinion formation. We consider a large interacting agent
system, and assume that agent interactions are driven by compromise as well as
self-thinking dynamics and also modulated by an underlying static social
network. This network structure is included using so-called graphons, which
modulate the interaction frequency in the corresponding kinetic formulation. We
then derive the corresponding limiting Fokker Planck equation, and analyze its
large time behavior. This microscopic setting serves as a starting point for
the proposed control strategy, which steers agents away from mean opinion and
is characterised by a suitable penalization depending on the properties of the
graphon. We show that this minimalist approach is very effective by analyzing
the quasi-stationary solutions mean-field model in a plurality of graphon
structures. Several numerical experiments are also provided to show the
effectiveness of the approach in preventing the formation of consensus steering
the system towards a declustered state.
