---
_id: '59171'
abstract:
- lang: eng
  text: To model dynamical systems on networks with higher-order (non-pairwise) interactions,
    we recently introduced a new class of ordinary differential equations (ODEs) on
    hypernetworks. Here, we consider one-parameter synchrony breaking bifurcations
    in such ODEs. We call a synchrony breaking steady-state branch ‘reluctant’ if
    it is tangent to a synchrony space, but does not lie inside it. We prove that
    reluctant synchrony breaking is ubiquitous in hypernetwork systems, by constructing
    a large class of examples that support it. We also give an explicit formula for
    the order of tangency to the synchrony space of a reluctant steady-state branch.
author:
- first_name: Sören
  full_name: von der Gracht, Sören
  id: '97359'
  last_name: von der Gracht
  orcid: 0000-0002-8054-2058
- first_name: Eddie
  full_name: Nijholt, Eddie
  last_name: Nijholt
- first_name: Bob
  full_name: Rink, Bob
  last_name: Rink
citation:
  ama: 'von der Gracht S, Nijholt E, Rink B. Higher-order interactions lead to ‘reluctant’
    synchrony breaking. <i>Proceedings of the Royal Society A: Mathematical, Physical
    and Engineering Sciences</i>. 2024;480(2301). doi:<a href="https://doi.org/10.1098/rspa.2023.0945">10.1098/rspa.2023.0945</a>'
  apa: 'von der Gracht, S., Nijholt, E., &#38; Rink, B. (2024). Higher-order interactions
    lead to ‘reluctant’ synchrony breaking. <i>Proceedings of the Royal Society A:
    Mathematical, Physical and Engineering Sciences</i>, <i>480</i>(2301). <a href="https://doi.org/10.1098/rspa.2023.0945">https://doi.org/10.1098/rspa.2023.0945</a>'
  bibtex: '@article{von der Gracht_Nijholt_Rink_2024, title={Higher-order interactions
    lead to ‘reluctant’ synchrony breaking}, volume={480}, DOI={<a href="https://doi.org/10.1098/rspa.2023.0945">10.1098/rspa.2023.0945</a>},
    number={2301}, journal={Proceedings of the Royal Society A: Mathematical, Physical
    and Engineering Sciences}, publisher={The Royal Society}, author={von der Gracht,
    Sören and Nijholt, Eddie and Rink, Bob}, year={2024} }'
  chicago: 'Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “Higher-Order Interactions
    Lead to ‘Reluctant’ Synchrony Breaking.” <i>Proceedings of the Royal Society A:
    Mathematical, Physical and Engineering Sciences</i> 480, no. 2301 (2024). <a href="https://doi.org/10.1098/rspa.2023.0945">https://doi.org/10.1098/rspa.2023.0945</a>.'
  ieee: 'S. von der Gracht, E. Nijholt, and B. Rink, “Higher-order interactions lead
    to ‘reluctant’ synchrony breaking,” <i>Proceedings of the Royal Society A: Mathematical,
    Physical and Engineering Sciences</i>, vol. 480, no. 2301, 2024, doi: <a href="https://doi.org/10.1098/rspa.2023.0945">10.1098/rspa.2023.0945</a>.'
  mla: 'von der Gracht, Sören, et al. “Higher-Order Interactions Lead to ‘Reluctant’
    Synchrony Breaking.” <i>Proceedings of the Royal Society A: Mathematical, Physical
    and Engineering Sciences</i>, vol. 480, no. 2301, The Royal Society, 2024, doi:<a
    href="https://doi.org/10.1098/rspa.2023.0945">10.1098/rspa.2023.0945</a>.'
  short: 'S. von der Gracht, E. Nijholt, B. Rink, Proceedings of the Royal Society
    A: Mathematical, Physical and Engineering Sciences 480 (2024).'
date_created: 2025-03-27T10:15:06Z
date_updated: 2025-03-27T10:19:56Z
ddc:
- '510'
department:
- _id: '101'
doi: 10.1098/rspa.2023.0945
file:
- access_level: open_access
  content_type: application/pdf
  creator: svdg
  date_created: 2025-03-27T10:16:20Z
  date_updated: 2025-03-27T10:19:48Z
  file_id: '59172'
  file_name: higher-order-interactions-lead-to-reluctant-synchrony-breaking.pdf
  file_size: 820435
  relation: main_file
file_date_updated: 2025-03-27T10:19:48Z
has_accepted_license: '1'
intvolume: '       480'
issue: '2301'
keyword:
- higher-order interactions
- synchrony breaking
- network dynamics
- coupled cell systems
language:
- iso: eng
oa: '1'
publication: 'Proceedings of the Royal Society A: Mathematical, Physical and Engineering
  Sciences'
publication_identifier:
  issn:
  - 1364-5021
  - 1471-2946
publication_status: published
publisher: The Royal Society
status: public
title: Higher-order interactions lead to ‘reluctant’ synchrony breaking
type: journal_article
user_id: '97359'
volume: 480
year: '2024'
...