Modul:   MAT975  Research Seminar in Network Science

Group interactions in networked systems: No higher-order effects without non-linearity!

Vortrag von Leonie Neuhäuser

Sprecher eingeladen von: Prof. Dr. Alexandre Bovet

Datum: 19.06.23  Zeit: 14.00 - 15.00  Raum: Y27H25

Networks provide a powerful framework for the modelling of dynamical systems. However, it is increasingly realised that such pairwise interaction models may not be sufficient to describe a range of important phenomena which are determined by group interactions, ranging from social groups to neuronal activity interactions. In this talk, we derive and analyse 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, regardless of the underlying multibody structure.We thus focus on dynamics based on a certain class of non-linear interaction functions, which can model different sociological phenomena such as peer pressure and stubbornness. Unlike for linear consensus dynamics on networks, we show how our nonlinear model dynamics can cause shifts away from the average system state. Extending our work to the case of temporal group interactions, we find interaction effects between the polyadic and temporal dimension that result in a first-mover advantage in the consensus formation process: If there is a local majority opinion in the hyperedges that are active early on, then the majority in these first-mover groups has a higher influence on the final consensus value—a behaviour that is not observable in this form in projections of the temporal hypergraph. Our results show that when accounting for group interactions in networked systems, one has to take into account the type of dynamics present: there are no higher-order effects without non-linearity!