Consensus dynamics on temporal hypergraphs

Physical review. E, vol. 104, pp. 064305

Abstract

We investigate consensus dynamics on temporal hypergraphs that encode network systems with time-dependent, multiway interactions. We compare these consensus processes with dynamics evolving on projections that remove the temporal and/or the multiway interactions of the higher-order network representation. For linear average consensus dynamics, we find that the convergence of a randomly switching time-varying system with multiway interactions is slower than the convergence of the corresponding system with pairwise interactions, which in turn exhibits a slower convergence rate than a consensus dynamics on the corresponding static network. We then consider a nonlinear consensus dynamics model in the temporal setting. Here we find that in addition to an effect on the convergence speed, the final consensus value of the temporal system can differ strongly from the consensus on the aggregated, static hypergraph. In particular, we observe 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 behavior that is not observable in this form in projections of the temporal hypergraph.

Authors 3

1. Leonie Neuhäuser Aachen Department of Computer Science

   RWTH Aachen University

   Affiliation as printed

   Department of Computer Science, RWTH Aachen University, 52074 Aachen, Germany

   RWTH Aachen University

2. Renaud Lambiotte

   University of Oxford

   Affiliation as printed

   Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom

   University of Oxford

3. Michael T. Schaub Aachen Department of Computer Science

   RWTH Aachen University

   Affiliation as printed

   Department of Computer Science, RWTH Aachen University, 52074 Aachen, Germany

   RWTH Aachen University