Tuesday 22 Mar 2022: Consensus dynamics on temporal hypergraphs
Renaud Lambiotte - University of Oxford
https://Universityofexeter.zoom.us/j/98128535238?pwd=b1NNR1MwV295VHRWWFh4b1NDTjJoZz09 Meeting ID: 981 2853 5238 Password: 561487 13:30-14:30
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.