Network dynamics with higher-order interactions: coupled cell hypernetworks for identical cells and synchrony

Journal article

Many networked systems are governed by non-pairwise interactions between nodes. The resulting higher-order interaction structure can then be encoded by means of a hypernetwork. In this paper we consider dynamical systems on hypernetworks by defining a class of admissible maps for every such hypernetwork. We explain how to classify robust cluster synchronization patterns on hypernetworks by finding balanced partitions, and we generalize the concept of a graph fibration to the hypernetwork context. We also show that robust synchronization patterns are only fully determined by polynomial admissible maps of high order. This means that, unlike in dyadic networks, cluster synchronization on hypernetworks is a higher-order, i.e., nonlinear, effect. We give a formula, in terms of the order of the hypernetwork, for the degree of the polynomial admissible maps that determine robust synchronization patterns. We also demonstrate that this degree is optimal by investigating a class of examples. We conclude by demonstrating how this effect may cause remarkable synchrony breaking bifurcations that occur at high polynomial degree.

Authors: Aguiar, M; Bick, C; Dias, A

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: IOP Publishing
• Journal: Nonlinearity
• Volume: 36
• Issue: 9
• Pages: 4641-4673
• Publication date: 2023-07-24
• DOI: 10.1088/1361-6544/ace39f
• EISSN: 1361-6544
• ISSN: 0951-7715
• Language: English
• Keywords: Bipartite graph; Graph; Subspace topology; Digraph; Nonlinear system; Physics; Theoretical computer science; Hypergraph; Mathematics; Pure mathematics; Linear subspace; Computer science; Combinatorics; Topology (electrical circuits); Transitive relation