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In this paper, we explore the non-linear dynamics of consensus on hypergraphs, extending the previously introduced three-body consensus model (3CM) to hyperedges of any cardinality.

In this work, we derive and analyze models for consensus dynamics on hypergraphs, where nodes interact in groups rather than in pairs. Our work reveals that multibody dynamical effects that go beyond rescaled pairwise interactions can appear only if the interaction function is nonlinear.