Multi-population phase oscillator networks with higher-order interactions

Journal article

Heteroclinic structures organize global features of dynamical systems. We analyze whether heteroclinic structures can arise in network dynamics with higher-order interactions which describe the nonlinear interactions between three or more units. We find that while commonly analyzed model equations such as network dynamics on undirected hypergraphs may be useful to describe local dynamics such as cluster synchronization, they give rise to obstructions that allow to design heteroclinic structures in phase space. By contrast, directed hypergraphs break the homogeneity and lead to vector fields that support heteroclinic structures.Comment: 38 pages, 4 Figure

Authors: Bick, C; Böhle, T; Kuehn, C

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Nonlinear Differential Equations and Applications
• Volume: 29
• Issue: 6
• Pages: 64
• Article number: 64
• Publication date: 2022-08-12
• DOI: 10.1007/s00030-022-00796-x
• EISSN: 1420-9004
• ISSN: 1021-9722
• Language: English
• Keywords: Statistical physics; Computer science; Invariant (physics); Stability (learning theory); Synchronization (alternating current); Topology (electrical circuits); Population; Field (mathematics); Applied mathematics; Quantum mechanics; Physics; Mean field theory; Pairwise comparison; Kuramoto model; Coupling (piping); Pure mathematics; Dynamical systems theory; Mathematics