---
_id: '52726'
abstract:
- lang: eng
  text: Heteroclinic structures organize global features of dynamical systems. We
    analyse 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 analysed 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 of heteroclinic
    structures in phase space. By contrast, directed hypergraphs break the homogeneity
    and lead to vector fields that support heteroclinic structures.
article_type: original
author:
- first_name: Christian
  full_name: Bick, Christian
  last_name: Bick
- first_name: Sören
  full_name: von der Gracht, Sören
  id: '97359'
  last_name: von der Gracht
  orcid: 0000-0002-8054-2058
citation:
  ama: Bick C, von der Gracht S. Heteroclinic dynamics in network dynamical systems
    with higher-order interactions. <i>Journal of Complex Networks</i>. 2024;12(2).
    doi:<a href="https://doi.org/10.1093/comnet/cnae009">10.1093/comnet/cnae009</a>
  apa: Bick, C., &#38; von der Gracht, S. (2024). Heteroclinic dynamics in network
    dynamical systems with higher-order interactions. <i>Journal of Complex Networks</i>,
    <i>12</i>(2). <a href="https://doi.org/10.1093/comnet/cnae009">https://doi.org/10.1093/comnet/cnae009</a>
  bibtex: '@article{Bick_von der Gracht_2024, title={Heteroclinic dynamics in network
    dynamical systems with higher-order interactions}, volume={12}, DOI={<a href="https://doi.org/10.1093/comnet/cnae009">10.1093/comnet/cnae009</a>},
    number={2}, journal={Journal of Complex Networks}, publisher={Oxford University
    Press (OUP)}, author={Bick, Christian and von der Gracht, Sören}, year={2024}
    }'
  chicago: Bick, Christian, and Sören von der Gracht. “Heteroclinic Dynamics in Network
    Dynamical Systems with Higher-Order Interactions.” <i>Journal of Complex Networks</i>
    12, no. 2 (2024). <a href="https://doi.org/10.1093/comnet/cnae009">https://doi.org/10.1093/comnet/cnae009</a>.
  ieee: 'C. Bick and S. von der Gracht, “Heteroclinic dynamics in network dynamical
    systems with higher-order interactions,” <i>Journal of Complex Networks</i>, vol.
    12, no. 2, 2024, doi: <a href="https://doi.org/10.1093/comnet/cnae009">10.1093/comnet/cnae009</a>.'
  mla: Bick, Christian, and Sören von der Gracht. “Heteroclinic Dynamics in Network
    Dynamical Systems with Higher-Order Interactions.” <i>Journal of Complex Networks</i>,
    vol. 12, no. 2, Oxford University Press (OUP), 2024, doi:<a href="https://doi.org/10.1093/comnet/cnae009">10.1093/comnet/cnae009</a>.
  short: C. Bick, S. von der Gracht, Journal of Complex Networks 12 (2024).
date_created: 2024-03-22T09:04:57Z
date_updated: 2024-03-22T09:11:53Z
ddc:
- '510'
department:
- _id: '101'
doi: 10.1093/comnet/cnae009
external_id:
  arxiv:
  - '2309.02006'
file:
- access_level: closed
  content_type: application/pdf
  creator: svdg
  date_created: 2024-03-22T09:06:07Z
  date_updated: 2024-03-22T09:06:07Z
  file_id: '52728'
  file_name: heteroclinic-dynamics-in-network-dynamical-systems-with-higher-order-interactions.pdf
  file_size: 649155
  relation: main_file
  success: 1
file_date_updated: 2024-03-22T09:06:07Z
has_accepted_license: '1'
intvolume: '        12'
issue: '2'
keyword:
- Applied Mathematics
- Computational Mathematics
- Control and Optimization
- Management Science and Operations Research
- Computer Networks and Communications
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://academic.oup.com/comnet/article-pdf/12/2/cnae009/56832119/cnae009.pdf
oa: '1'
publication: Journal of Complex Networks
publication_identifier:
  issn:
  - 2051-1329
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Heteroclinic dynamics in network dynamical systems with higher-order interactions
type: journal_article
user_id: '97359'
volume: 12
year: '2024'
...