---
res:
bibo_abstract:
- 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.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Sören
foaf_name: von der Gracht, Sören
foaf_surname: von der Gracht
foaf_workInfoHomepage: http://www.librecat.org/personId=97359
orcid: 0000-0002-8054-2058
- foaf_Person:
foaf_givenName: Eddie
foaf_name: Nijholt, Eddie
foaf_surname: Nijholt
- foaf_Person:
foaf_givenName: Bob
foaf_name: Rink, Bob
foaf_surname: Rink
bibo_doi: 10.1137/23m1561075
bibo_issue: '6'
bibo_volume: 83
dct_date: 2023^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/0036-1399
- http://id.crossref.org/issn/1095-712X
dct_language: eng
dct_publisher: Society for Industrial & Applied Mathematics (SIAM)@
dct_subject:
- Applied Mathematics
dct_title: 'Hypernetworks: Cluster Synchronization Is a Higher-Order Effect@'
...