  The basic interaction unit of many dynamical systems involves more than two
nodes. In such situations where networks are not an appropriate modelling
framework, it has recently become increasingly popular to turn to higher-order
models, including hypergraphs. In this paper, we explore the non-linear
dynamics of consensus on hypergraphs, allowing for interactions within
hyperedges of any cardinality. After discussing the different ways in which
non-linearities can be incorporated in the dynamical model, building on
different sociological theories, we explore its mathematical properties and
perform simulations to investigate them numerically. After focussing on
synthetic hypergraphs, namely on block hypergraphs, we investigate the dynamics
on real-world structures, and explore in detail the role of involvement and
stubbornness on polarisation.
