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On the convergence of nonlinear averaging dynamics with three-body interactions on hypergraphs. (arXiv:2304.07203v1 [math.DS])
cs.LG updates on arXiv.org arxiv.org
Complex networked systems in fields such as physics, biology, and social
sciences often involve interactions that extend beyond simple pairwise ones.
Hypergraphs serve as powerful modeling tools for describing and analyzing the
intricate behaviors of systems with multi-body interactions. Herein, we
investigate a discrete-time nonlinear averaging dynamics with three-body
interactions: an underlying hypergraph, comprising triples as hyperedges,
delineates the structure of these interactions, while the vertices update their
states through a weighted, state-dependent average of neighboring pairs'
states. This dynamics …
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