Traditional networks, encoding pairwise interactions between units, have proved a powerful tool to model complex dynamical systems. However, dynamical units can generally interact in groups of more than two at a time, and that information is not encoded. Importantly, these group interactions can impact the dynamics of the system and the nature of its transitions, as shown by recent studies. In particular, for synchronisation, group interactions e.g. promote clusters and abrupt transitions. We will discuss recent advances on the topic, and in particular the multiorder Laplacian -- a generalisation of the graph Laplacian that includes group interactions. In addition, we will discuss how we used it to investigate whether group interactions always enhance synchronisation, and how the choice of their representation -- hypergraph or simplicial complex -- influences the dynamics.
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