TY - JOUR A1 - Neuhäuser, Leonie A1 - Mellor, Andrew A1 - Lambiotte, Renaud T1 - Multi-body Interactions and Non-Linear Consensus Dynamics on Networked Systems JF - Physical Review E N2 - Multi-body interactions can reveal higher-order dynamical effects that are not captured by traditional two-body network models. In this work, we derive and analyse models for consensus dynamics on hypergraphs, where nodes interact in groups rather than in pairs. Our work reveals that multi-body dynamical effects that go beyond rescaled pairwise interactions can only appear if the interaction function is non-linear, regardless of the underlying multi-body structure. As a practical application, we introduce a specific non-linear function to model three-body consensus, which incorporates reinforcing group effects such as peer pressure. Unlike consensus processes on networks, we find that the resulting dynamics can cause shifts away from the average system state. The nature of these shifts depends on a complex interplay between the distribution of the initial states, the underlying structure and the form of the interaction function. By considering modular hypergraphs, we discover state-dependent, asymmetric dynamics between polarised clusters where multi-body interactions make one cluster dominate the other. KW - Collective behavior in networks KW - Community structure KW - Patterns in complex systems KW - Spreading Y1 - 2020 U6 - https://doi.org/10.1103/PhysRevE.101.032310 SN - 2470-0053 VL - 101 IS - 3 ER - TY - INPR A1 - Neuhäuser, Leonie A1 - Schaub, Michael A1 - Mellor, Andrew A1 - Lambiotte, Renaud T1 - Opinion Dynamics with Multi-Body Interactions T2 - Physics and Society (physics.soc-ph) N2 - We introduce and analyse a three-body consensus model (3CM) for non-linear consensus dynamics on hypergraphs. Our model incorporates reinforcing group effects, which can cause shifts in the average state of the system even in if the underlying graph is complete (corresponding to a mean-field interaction), a phenomena that may be interpreted as a type of peer pressure. We further demonstrate that for systems with two clustered groups, already a small asymmetry in our dynamics can lead to the opinion of one group becoming clearly dominant. We show that the nonlinearity in the model is the essential ingredient to make such group dynamics appear, and demonstrate how our system can otherwise be written as a linear, pairwise interaction system on a rescaled network. Y1 - 2021 UR - https://arxiv.org/abs/2004.00901 ET - arXiv:2004.00901 [physics.soc-ph] ER -