Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session Z09: Higher-Order Interactions: The Next Frontier of Complex Systems
11:30 AM–2:18 PM,
Friday, March 18, 2022
Room: McCormick Place W-180
Sponsoring Units: GSNP DCOMP
Chair: Yuanzhao Zhang, Santa Fe Institute
Abstract: Z09.00001 : Consensus dynamics and opinion formation on hypergraphs*
11:30 AM–12:06 PM
(University of Namur)
(University of Namur)
As a first step, we introduce models for consensus on hypergraphs, showing that non-linearity is necessary to observe non-trivial many-body effects.
We compare the dynamics with that on appropriate projections of this higher-order network representation that flatten the temporal, the multi-way component, or both.
For linear average consensus dynamics, we find that the convergence of a randomly switching time-varying system with multi-way 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, 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.
*RL acknowledges support from the EPSRC Grants No.EP/V013068/1 and EP/V03474X/1
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