Phase transitions and stability of dynamical processes on hypergraphs

• DOI: 10.1038/s42005-021-00525-3
• Publication Date: 2021-02-12T11:05:04Z
• Authors: Guilherme Ferraz ...; Michele Tizzani; Yamir Moreno
• Keywords: Hypergraph; Dynamical system (definition)

Abstract Hypergraphs naturally represent higher-order interactions, which persistently appear in social neural networks, and other natural systems. Although their importance is well recognized, a theoretical framework to describe general dynamical processes on hypergraphs not available yet. In this paper, we derive expressions for the stability of systems defined an arbitrary hypergraph. The allows us reveal that, near fixed point, relevant structure weighted graph-projection hypergraph that it possible identify role each structural order given process. We analytically solve two dynamics interest, namely, contagion diffusion processes, show conditions can be decoupled components. Our results process, only pairwise interactions play absorbing state, while dynamics, plays differential role. work provides further exploration hypergraphs.