---
_id: '64865'
abstract:
- lang: eng
text: We provide a method to systematically construct vector fields for which the
dynamics display transitions corresponding to a desired hierarchical connection
structure. This structure is given as a finite set of directed graphs $\mathbf{G}_1,\dotsc,\mathbf{G}_N$
(the lower level), together with another digraph $\mathbfΓ$ on $N$ vertices (the
top level). The dynamic realizations of $\mathbf{G}_1,\dotsc,\mathbf{G}_N$ are
heteroclinic networks and they can be thought of as individual connection patterns
on a given set of states. Edges in $\mathbfΓ$ correspond to transitions between
these different patterns. In our construction, the connections given through $\mathbfΓ$
are not heteroclinic, but excitable with zero threshold. This describes a dynamical
transition between two invariant sets where every $δ$-neighborhood of the first
set contains an initial condition with $ω$-limit in the second set. Thus, we prove
a theorem that allows the systematic creation of hierarchical networks that are
excitable on the top level, and heteroclinic on the lower level. Our results modify
and extend the simplex realization method by Ashwin & Postlethwaite.
author:
- first_name: Sören
full_name: von der Gracht, Sören
id: '97359'
last_name: von der Gracht
orcid: 0000-0002-8054-2058
- first_name: Alexander
full_name: Lohse, Alexander
last_name: Lohse
citation:
ama: von der Gracht S, Lohse A. Design of Hierarchical Excitable Networks. arXiv:260306157.
Published online 2026.
apa: von der Gracht, S., & Lohse, A. (2026). Design of Hierarchical Excitable
Networks. In arXiv:2603.06157.
bibtex: '@article{von der Gracht_Lohse_2026, title={Design of Hierarchical Excitable
Networks}, journal={arXiv:2603.06157}, author={von der Gracht, Sören and Lohse,
Alexander}, year={2026} }'
chicago: Gracht, Sören von der, and Alexander Lohse. “Design of Hierarchical Excitable
Networks.” ArXiv:2603.06157, 2026.
ieee: S. von der Gracht and A. Lohse, “Design of Hierarchical Excitable Networks,”
arXiv:2603.06157. 2026.
mla: von der Gracht, Sören, and Alexander Lohse. “Design of Hierarchical Excitable
Networks.” ArXiv:2603.06157, 2026.
short: S. von der Gracht, A. Lohse, ArXiv:2603.06157 (2026).
date_created: 2026-03-09T08:22:58Z
date_updated: 2026-03-09T08:26:49Z
ddc:
- '510'
department:
- _id: '101'
- _id: '841'
external_id:
arxiv:
- '2603.06157'
file:
- access_level: closed
content_type: application/pdf
creator: svdg
date_created: 2026-03-09T08:26:04Z
date_updated: 2026-03-09T08:26:04Z
file_id: '64866'
file_name: design-of-hierarchical-excitable-networks.pdf
file_size: 5179491
relation: main_file
success: 1
file_date_updated: 2026-03-09T08:26:04Z
has_accepted_license: '1'
language:
- iso: eng
publication: arXiv:2603.06157
related_material:
link:
- relation: research_paper
url: https://s-vdg.github.io/publication/design-of-hierarchical-excitable-networks/design-of-hierarchical-excitable-networks.pdf
status: public
title: Design of Hierarchical Excitable Networks
type: preprint
user_id: '97359'
year: '2026'
...
---
_id: '64979'
abstract:
- lang: eng
text: We investigate homogeneous coupled cell systems with high-dimensional internal
dynamics. In many studies on network dynamics, the analysis is restricted to networks
with one-dimensional internal dynamics. Here, we show how symmetry explains the
relation between dynamical behavior of systems with one-dimensional internal dynamics
and with higher dimensional internal dynamics, when the underlying network topology
is the same. Fundamental networks of homogeneous coupled cell systems (B. Rink,
J. Sanders. Coupled Cell Networks and Their Hidden Symmetries. SIAM J. Math. Anal.
46.2 (2014)) can be expressed in terms of monoid representations, which uniquely
decompose into indecomposable subrepresentations. In the high-dimensional internal
dynamics case, these subrepresentations are isomorphic to multiple copies of those
one computes in the one-dimensional internal dynamics case. This has interesting
implications for possible center subspaces in bifurcation analysis. We describe
the effect on steady state and Hopf bifurcations in l-parameter families of network
vector fields. The main results in that regard are that (1) generic one-parameter
steady state bifurcations are qualitatively independent of the dimension of the
internal dynamics and that, (2) in order to observe all generic l-parameter bifurcations
that may occur for internal dynamics of any dimension, the internal dynamics has
to be at least l-dimensional for steady state bifurcations and 2l-dimensional
for Hopf bifurcations. Furthermore, we illustrate how additional structure in
the network can be exploited to obtain even greater understanding of bifurcation
scenarios in the high-dimensional case beyond qualitative statements about the
collective dynamics. One-parameter steady state bifurcations in feedforward networks
exhibit an unusual amplification in the asymptotic growth rates of individual
cells, when these are one-dimensional (S. von der Gracht, E. Nijholt, B. Rink.
Amplified steady state bifurcations in feedforward networks. Nonlinearity 35.4
(2022)). As another main result, we prove that (3) the same cells exhibit this
amplifying effect with the same growth rates when the internal dynamics is high-dimensional.
article_number: '118196'
article_type: original
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. Homogeneous coupled cell systems with
high-dimensional internal dynamics. Chaos, Solitons & Fractals. 2026;208.
doi:10.1016/j.chaos.2026.118196
apa: von der Gracht, S., Nijholt, E., & Rink, B. (2026). Homogeneous coupled
cell systems with high-dimensional internal dynamics. Chaos, Solitons &
Fractals, 208, Article 118196. https://doi.org/10.1016/j.chaos.2026.118196
bibtex: '@article{von der Gracht_Nijholt_Rink_2026, title={Homogeneous coupled cell
systems with high-dimensional internal dynamics}, volume={208}, DOI={10.1016/j.chaos.2026.118196},
number={118196}, journal={Chaos, Solitons & Fractals}, publisher={Elsevier
BV}, author={von der Gracht, Sören and Nijholt, Eddie and Rink, Bob}, year={2026}
}'
chicago: Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “Homogeneous Coupled
Cell Systems with High-Dimensional Internal Dynamics.” Chaos, Solitons &
Fractals 208 (2026). https://doi.org/10.1016/j.chaos.2026.118196.
ieee: 'S. von der Gracht, E. Nijholt, and B. Rink, “Homogeneous coupled cell systems
with high-dimensional internal dynamics,” Chaos, Solitons & Fractals,
vol. 208, Art. no. 118196, 2026, doi: 10.1016/j.chaos.2026.118196.'
mla: von der Gracht, Sören, et al. “Homogeneous Coupled Cell Systems with High-Dimensional
Internal Dynamics.” Chaos, Solitons & Fractals, vol. 208, 118196, Elsevier
BV, 2026, doi:10.1016/j.chaos.2026.118196.
short: S. von der Gracht, E. Nijholt, B. Rink, Chaos, Solitons & Fractals 208
(2026).
date_created: 2026-03-16T08:39:07Z
date_updated: 2026-03-16T08:42:56Z
ddc:
- '510'
department:
- _id: '101'
- _id: '841'
doi: 10.1016/j.chaos.2026.118196
external_id:
arxiv:
- '2510.06740'
file:
- access_level: closed
content_type: application/pdf
creator: svdg
date_created: 2026-03-16T08:40:04Z
date_updated: 2026-03-16T08:40:04Z
file_id: '64980'
file_name: homogeneous-coupled-cell-systems-with-high-dimensional-internal-dynamics.pdf
file_size: 1951746
relation: main_file
success: 1
file_date_updated: 2026-03-16T08:40:04Z
has_accepted_license: '1'
intvolume: ' 208'
keyword:
- Coupled cell systems
- Network dynamics
- Dimension reduction
- Bifurcation theory
- Symmetry
- Monoid representation theory
language:
- iso: eng
publication: Chaos, Solitons & Fractals
publication_identifier:
issn:
- 0960-0779
publication_status: published
publisher: Elsevier BV
status: public
title: Homogeneous coupled cell systems with high-dimensional internal dynamics
type: journal_article
user_id: '97359'
volume: 208
year: '2026'
...
---
_id: '66057'
author:
- first_name: Nils
full_name: Bullerjahn, Nils
id: '103797'
last_name: Bullerjahn
orcid: https://orcid.org/0009-0003-8460-1574
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
citation:
ama: Bullerjahn N, Kovács B. Error estimates for $A$-stable backward difference
full discretizations of Willmore flow of closed surfaces. ArXiv. Published
online 2026. doi:10.48550/arXiv.2606.25934
apa: Bullerjahn, N., & Kovács, B. (2026). Error estimates for $A$-stable backward
difference full discretizations of Willmore flow of closed surfaces. ArXiv.
https://doi.org/10.48550/arXiv.2606.25934
bibtex: '@article{Bullerjahn_Kovács_2026, title={Error estimates for $A$-stable
backward difference full discretizations of Willmore flow of closed surfaces},
DOI={10.48550/arXiv.2606.25934},
journal={ArXiv}, author={Bullerjahn, Nils and Kovács, Balázs}, year={2026} }'
chicago: Bullerjahn, Nils, and Balázs Kovács. “Error Estimates for $A$-Stable Backward
Difference Full Discretizations of Willmore Flow of Closed Surfaces.” ArXiv,
2026. https://doi.org/10.48550/arXiv.2606.25934.
ieee: 'N. Bullerjahn and B. Kovács, “Error estimates for $A$-stable backward difference
full discretizations of Willmore flow of closed surfaces,” ArXiv, 2026,
doi: 10.48550/arXiv.2606.25934.'
mla: Bullerjahn, Nils, and Balázs Kovács. “Error Estimates for $A$-Stable Backward
Difference Full Discretizations of Willmore Flow of Closed Surfaces.” ArXiv,
2026, doi:10.48550/arXiv.2606.25934.
short: N. Bullerjahn, B. Kovács, ArXiv (2026).
date_created: 2026-06-26T06:03:08Z
date_updated: 2026-06-26T06:09:29Z
department:
- _id: '841'
doi: 10.48550/arXiv.2606.25934
language:
- iso: eng
publication: ArXiv
status: public
title: Error estimates for $A$-stable backward difference full discretizations of
Willmore flow of closed surfaces
type: journal_article
user_id: '103797'
year: '2026'
...
---
_id: '60048'
author:
- first_name: Raphael
full_name: Gerlach, Raphael
id: '32655'
last_name: Gerlach
orcid: 0009-0002-4750-2051
- first_name: Sören
full_name: von der Gracht, Sören
id: '97359'
last_name: von der Gracht
orcid: 0000-0002-8054-2058
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: 'Gerlach R, von der Gracht S, Dellnitz M. On the Dynamical Hierarchy in Gathering
Protocols with Circulant Topologies. In: Lecture Notes in Computer Science.
Springer Nature Switzerland; 2025. doi:10.1007/978-3-031-91736-3_19'
apa: Gerlach, R., von der Gracht, S., & Dellnitz, M. (2025). On the Dynamical
Hierarchy in Gathering Protocols with Circulant Topologies. In Lecture Notes
in Computer Science. Springer Nature Switzerland. https://doi.org/10.1007/978-3-031-91736-3_19
bibtex: '@inbook{Gerlach_von der Gracht_Dellnitz_2025, place={Cham}, title={On the Dynamical
Hierarchy in Gathering Protocols with Circulant Topologies}, DOI={10.1007/978-3-031-91736-3_19},
booktitle={Lecture Notes in Computer Science}, publisher={Springer Nature Switzerland},
author={Gerlach, Raphael and von der Gracht, Sören and Dellnitz, Michael}, year={2025}
}'
chicago: 'Gerlach, Raphael, Sören von der Gracht, and Michael Dellnitz. “On the Dynamical
Hierarchy in Gathering Protocols with Circulant Topologies.” In Lecture Notes
in Computer Science. Cham: Springer Nature Switzerland, 2025. https://doi.org/10.1007/978-3-031-91736-3_19.'
ieee: 'R. Gerlach, S. von der Gracht, and M. Dellnitz, “On the Dynamical Hierarchy
in Gathering Protocols with Circulant Topologies,” in Lecture Notes in Computer
Science, Cham: Springer Nature Switzerland, 2025.'
mla: Gerlach, Raphael, et al. “On the Dynamical Hierarchy in Gathering Protocols
with Circulant Topologies.” Lecture Notes in Computer Science, Springer
Nature Switzerland, 2025, doi:10.1007/978-3-031-91736-3_19.
short: 'R. Gerlach, S. von der Gracht, M. Dellnitz, in: Lecture Notes in Computer
Science, Springer Nature Switzerland, Cham, 2025.'
date_created: 2025-05-27T08:17:03Z
date_updated: 2025-05-27T08:22:42Z
department:
- _id: '101'
doi: 10.1007/978-3-031-91736-3_19
external_id:
arxiv:
- '2503.07576'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' ArXiv:2503.07576'
oa: '1'
place: Cham
project:
- _id: '106'
grant_number: '453112019'
name: 'Algorithmen für Schwarmrobotik: Verteiltes Rechnen trifft Dynamische Systeme'
publication: Lecture Notes in Computer Science
publication_identifier:
isbn:
- '9783031917356'
- '9783031917363'
issn:
- 0302-9743
- 1611-3349
publication_status: published
publisher: Springer Nature Switzerland
status: public
title: On the Dynamical Hierarchy in Gathering Protocols with Circulant Topologies
type: book_chapter
user_id: '32655'
year: '2025'
...
---
_id: '55459'
article_type: original
author:
- first_name: Nils
full_name: Bullerjahn, Nils
id: '103797'
last_name: Bullerjahn
orcid: https://orcid.org/0009-0003-8460-1574
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
citation:
ama: Bullerjahn N, Kovács B. Error estimates for full discretization of Cahn--Hilliard
equation with dynamic boundary conditions. IMA Journal of Numerical Analysis.
doi:10.1093/imanum/draf009
apa: Bullerjahn, N., & Kovács, B. (n.d.). Error estimates for full discretization
of Cahn--Hilliard equation with dynamic boundary conditions. IMA Journal of
Numerical Analysis. https://doi.org/10.1093/imanum/draf009
bibtex: '@article{Bullerjahn_Kovács, title={Error estimates for full discretization
of Cahn--Hilliard equation with dynamic boundary conditions}, DOI={10.1093/imanum/draf009},
journal={IMA Journal of Numerical Analysis}, author={Bullerjahn, Nils and Kovács,
Balázs} }'
chicago: Bullerjahn, Nils, and Balázs Kovács. “Error Estimates for Full Discretization
of Cahn--Hilliard Equation with Dynamic Boundary Conditions.” IMA Journal of
Numerical Analysis, n.d. https://doi.org/10.1093/imanum/draf009.
ieee: 'N. Bullerjahn and B. Kovács, “Error estimates for full discretization of
Cahn--Hilliard equation with dynamic boundary conditions,” IMA Journal of Numerical
Analysis, doi: 10.1093/imanum/draf009.'
mla: Bullerjahn, Nils, and Balázs Kovács. “Error Estimates for Full Discretization
of Cahn--Hilliard Equation with Dynamic Boundary Conditions.” IMA Journal of
Numerical Analysis, doi:10.1093/imanum/draf009.
short: N. Bullerjahn, B. Kovács, IMA Journal of Numerical Analysis (n.d.).
date_created: 2024-07-31T09:03:45Z
date_updated: 2026-02-18T14:46:18Z
department:
- _id: '841'
doi: 10.1093/imanum/draf009
language:
- iso: eng
publication: IMA Journal of Numerical Analysis
publication_status: accepted
status: public
title: Error estimates for full discretization of Cahn--Hilliard equation with dynamic
boundary conditions
type: journal_article
user_id: '100441'
year: '2025'
...
---
_id: '53141'
author:
- first_name: Dominik
full_name: Edelmann, Dominik
last_name: Edelmann
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
- first_name: Christian
full_name: Lubich, Christian
last_name: Lubich
citation:
ama: Edelmann D, Kovács B, Lubich C. Numerical analysis of an evolving bulk--surface
model of tumour growth. IMA Journal of Numerical Analysis. 2025;45(5):2581--2627.
doi:10.1093/imanum/drae077
apa: Edelmann, D., Kovács, B., & Lubich, C. (2025). Numerical analysis of an
evolving bulk--surface model of tumour growth. IMA Journal of Numerical Analysis,
45(5), 2581--2627. https://doi.org/10.1093/imanum/drae077
bibtex: '@article{Edelmann_Kovács_Lubich_2025, title={Numerical analysis of an evolving
bulk--surface model of tumour growth}, volume={45}, DOI={10.1093/imanum/drae077},
number={5}, journal={IMA Journal of Numerical Analysis}, author={Edelmann, Dominik
and Kovács, Balázs and Lubich, Christian}, year={2025}, pages={2581--2627} }'
chicago: 'Edelmann, Dominik, Balázs Kovács, and Christian Lubich. “Numerical Analysis
of an Evolving Bulk--Surface Model of Tumour Growth.” IMA Journal of Numerical
Analysis 45, no. 5 (2025): 2581--2627. https://doi.org/10.1093/imanum/drae077.'
ieee: 'D. Edelmann, B. Kovács, and C. Lubich, “Numerical analysis of an evolving
bulk--surface model of tumour growth,” IMA Journal of Numerical Analysis,
vol. 45, no. 5, pp. 2581--2627, 2025, doi: 10.1093/imanum/drae077.'
mla: Edelmann, Dominik, et al. “Numerical Analysis of an Evolving Bulk--Surface
Model of Tumour Growth.” IMA Journal of Numerical Analysis, vol. 45, no.
5, 2025, pp. 2581--2627, doi:10.1093/imanum/drae077.
short: D. Edelmann, B. Kovács, C. Lubich, IMA Journal of Numerical Analysis 45 (2025)
2581--2627.
date_created: 2024-04-03T09:11:36Z
date_updated: 2026-02-18T14:44:54Z
department:
- _id: '841'
doi: 10.1093/imanum/drae077
intvolume: ' 45'
issue: '5'
language:
- iso: eng
page: 2581--2627
publication: IMA Journal of Numerical Analysis
status: public
title: Numerical analysis of an evolving bulk--surface model of tumour growth
type: journal_article
user_id: '100441'
volume: 45
year: '2025'
...
---
_id: '55781'
abstract:
- lang: eng
text: "In this paper, we prove that spatially semi-discrete evolving finite element\r\nmethod
for parabolic equations on a given evolving hypersurface of arbitrary\r\ndimensions
preserves the maximal $L^p$-regularity at the discrete level. We\r\nfirst establish
the results on a stationary surface and then extend them, via a\r\nperturbation
argument, to the case where the underlying surface is evolving\r\nunder a prescribed
velocity field. The proof combines techniques in evolving\r\nfinite element method,
properties of Green's functions on (discretised) closed\r\nsurfaces, and local
energy estimates for finite element methods"
author:
- first_name: Genming
full_name: Bai, Genming
last_name: Bai
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
- first_name: Buyang
full_name: Li, Buyang
last_name: Li
citation:
ama: Bai G, Kovács B, Li B. Maximal regularity of evolving FEMs for parabolic equations
on an evolving surface. IMA Journal of Numerical Analysis. Published online
2025. doi:10.1093/imanum/draf082.
apa: Bai, G., Kovács, B., & Li, B. (2025). Maximal regularity of evolving FEMs
for parabolic equations on an evolving surface. IMA Journal of Numerical Analysis.
https://doi.org/10.1093/imanum/draf082.
bibtex: '@article{Bai_Kovács_Li_2025, title={Maximal regularity of evolving FEMs
for parabolic equations on an evolving surface}, DOI={10.1093/imanum/draf082.},
journal={IMA Journal of Numerical Analysis}, author={Bai, Genming and Kovács,
Balázs and Li, Buyang}, year={2025} }'
chicago: Bai, Genming, Balázs Kovács, and Buyang Li. “Maximal Regularity of Evolving
FEMs for Parabolic Equations on an Evolving Surface.” IMA Journal of Numerical
Analysis, 2025. https://doi.org/10.1093/imanum/draf082.
ieee: 'G. Bai, B. Kovács, and B. Li, “Maximal regularity of evolving FEMs for parabolic
equations on an evolving surface,” IMA Journal of Numerical Analysis,
2025, doi: 10.1093/imanum/draf082.'
mla: Bai, Genming, et al. “Maximal Regularity of Evolving FEMs for Parabolic Equations
on an Evolving Surface.” IMA Journal of Numerical Analysis, 2025, doi:10.1093/imanum/draf082.
short: G. Bai, B. Kovács, B. Li, IMA Journal of Numerical Analysis (2025).
date_created: 2024-08-27T07:37:39Z
date_updated: 2026-02-18T14:47:34Z
department:
- _id: '841'
doi: 10.1093/imanum/draf082.
external_id:
arxiv:
- '2408.14096'
language:
- iso: eng
publication: IMA Journal of Numerical Analysis
status: public
title: Maximal regularity of evolving FEMs for parabolic equations on an evolving
surface
type: journal_article
user_id: '100441'
year: '2025'
...
---
_id: '56298'
abstract:
- lang: eng
text: "In the general pattern formation (GPF) problem, a swarm of simple autonomous,\r\ndisoriented
robots must form a given pattern. The robots' simplicity imply a\r\nstrong limitation:
When the initial configuration is rotationally symmetric,\r\nonly patterns with
a similar symmetry can be formed [Yamashita, Suzyuki; TCS\r\n2010]. The only known
algorithm to form large patterns with limited visibility\r\nand without memory
requires the robots to start in a near-gathering (a swarm of\r\nconstant diameter)
[Hahn et al.; SAND 2024]. However, not only do we not know\r\nany near-gathering
algorithm guaranteed to preserve symmetry but most natural\r\ngathering strategies
trivially increase symmetries [Castenow et al.; OPODIS\r\n2022].\r\n Thus, we
study near-gathering without changing the swarm's rotational\r\nsymmetry for disoriented,
oblivious robots with limited visibility (the\r\nOBLOT-model, see [Flocchini et
al.; 2019]). We introduce a technique based on\r\nthe theory of dynamical systems
to analyze how a given algorithm affects\r\nsymmetry and provide sufficient conditions
for symmetry preservation. Until\r\nnow, it was unknown whether the considered
OBLOT-model allows for any\r\nnon-trivial algorithm that always preserves symmetry.
Our first result shows\r\nthat a variant of Go-to-the-Average always preserves
symmetry but may sometimes\r\nlead to multiple, unconnected near-gathering clusters.
Our second result is a\r\nsymmetry-preserving near-gathering algorithm that works
on swarms with a convex\r\nboundary (the outer boundary of the unit disc graph)
and without holes (circles\r\nof diameter 1 inside the boundary without any robots)."
author:
- first_name: Raphael
full_name: Gerlach, Raphael
id: '32655'
last_name: Gerlach
orcid: 0009-0002-4750-2051
- first_name: Sören
full_name: von der Gracht, Sören
id: '97359'
last_name: von der Gracht
orcid: 0000-0002-8054-2058
- first_name: Christopher
full_name: Hahn, Christopher
last_name: Hahn
- first_name: Jonas
full_name: Harbig, Jonas
id: '47213'
last_name: Harbig
- first_name: Peter
full_name: Kling, Peter
last_name: Kling
citation:
ama: 'Gerlach R, von der Gracht S, Hahn C, Harbig J, Kling P. Symmetry Preservation
in Swarms of Oblivious Robots with Limited Visibility. In: Bonomi S, Galletta
L, Rivière Etienne, Schiavoni Valerio, eds. 28th International Conference
on Principles of Distributed Systems (OPODIS 2024). Vol 324. Leibniz International
Proceedings in Informatics (LIPIcs). Schloss Dagstuhl -- Leibniz-Zentrum für Informatik;
2025. doi:10.4230/LIPIcs.OPODIS.2024.13'
apa: Gerlach, R., von der Gracht, S., Hahn, C., Harbig, J., & Kling, P. (2025).
Symmetry Preservation in Swarms of Oblivious Robots with Limited Visibility.
In S. Bonomi, L. Galletta, Etienne Rivière, & Valerio Schiavoni (Eds.),
28th International Conference on Principles of Distributed Systems (OPODIS
2024) (Vol. 324). Schloss Dagstuhl -- Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.OPODIS.2024.13
bibtex: '@inproceedings{Gerlach_von der Gracht_Hahn_Harbig_Kling_2025, series={Leibniz
International Proceedings in Informatics (LIPIcs)}, title={Symmetry Preservation
in Swarms of Oblivious Robots with Limited Visibility}, volume={324}, DOI={10.4230/LIPIcs.OPODIS.2024.13},
booktitle={28th International Conference on Principles of Distributed Systems
(OPODIS 2024)}, publisher={Schloss Dagstuhl -- Leibniz-Zentrum für Informatik},
author={Gerlach, Raphael and von der Gracht, Sören and Hahn, Christopher and Harbig,
Jonas and Kling, Peter}, editor={Bonomi, Silvia and Galletta, Letterio and Rivière, Etienne
and Schiavoni, Valerio}, year={2025}, collection={Leibniz International Proceedings
in Informatics (LIPIcs)} }'
chicago: Gerlach, Raphael, Sören von der Gracht, Christopher Hahn, Jonas Harbig,
and Peter Kling. “Symmetry Preservation in Swarms of Oblivious Robots with Limited
Visibility.” In 28th International Conference on Principles of Distributed
Systems (OPODIS 2024), edited by Silvia Bonomi, Letterio Galletta, Etienne
Rivière, and Valerio Schiavoni, Vol. 324. Leibniz International Proceedings in
Informatics (LIPIcs). Schloss Dagstuhl -- Leibniz-Zentrum für Informatik, 2025.
https://doi.org/10.4230/LIPIcs.OPODIS.2024.13.
ieee: 'R. Gerlach, S. von der Gracht, C. Hahn, J. Harbig, and P. Kling, “Symmetry
Preservation in Swarms of Oblivious Robots with Limited Visibility,” in 28th
International Conference on Principles of Distributed Systems (OPODIS 2024),
Lucca, Italy, 2025, vol. 324, doi: 10.4230/LIPIcs.OPODIS.2024.13.'
mla: Gerlach, Raphael, et al. “Symmetry Preservation in Swarms of Oblivious Robots
with Limited Visibility.” 28th International Conference on Principles of Distributed
Systems (OPODIS 2024), edited by Silvia Bonomi et al., vol. 324, Schloss Dagstuhl
-- Leibniz-Zentrum für Informatik, 2025, doi:10.4230/LIPIcs.OPODIS.2024.13.
short: 'R. Gerlach, S. von der Gracht, C. Hahn, J. Harbig, P. Kling, in: S. Bonomi,
L. Galletta, Etienne Rivière, Valerio Schiavoni (Eds.), 28th International Conference
on Principles of Distributed Systems (OPODIS 2024), Schloss Dagstuhl -- Leibniz-Zentrum
für Informatik, 2025.'
conference:
end_date: 2024-12-13
location: Lucca, Italy
name: 28th International Conference on Principles of Distributed Systems (OPODIS
2024)
start_date: 2024-12-11
date_created: 2024-10-01T13:29:43Z
date_updated: 2025-01-09T11:39:19Z
department:
- _id: '101'
doi: 10.4230/LIPIcs.OPODIS.2024.13
editor:
- first_name: Silvia
full_name: Bonomi, Silvia
last_name: Bonomi
- first_name: Letterio
full_name: Galletta, Letterio
last_name: Galletta
- first_name: ' Etienne'
full_name: Rivière, Etienne
last_name: Rivière
- first_name: ' Valerio'
full_name: Schiavoni, Valerio
last_name: Schiavoni
external_id:
arxiv:
- '2409.19277'
intvolume: ' 324'
keyword:
- Swarm Algorithm
- Swarm Robots
- Distributed Algorithm
- Pattern Formation
- Limited Visibility
- Oblivious
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2409.19277
oa: '1'
project:
- _id: '106'
grant_number: '453112019'
name: 'Algorithmen für Schwarmrobotik: Verteiltes Rechnen trifft Dynamische Systeme'
publication: 28th International Conference on Principles of Distributed Systems (OPODIS
2024)
publication_identifier:
isbn:
- 978-3-95977-360-7
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl -- Leibniz-Zentrum für Informatik
series_title: Leibniz International Proceedings in Informatics (LIPIcs)
status: public
title: Symmetry Preservation in Swarms of Oblivious Robots with Limited Visibility
type: conference
user_id: '97359'
volume: 324
year: '2025'
...
---
_id: '58532'
author:
- first_name: Nils
full_name: Bullerjahn, Nils
id: '103797'
last_name: Bullerjahn
orcid: https://orcid.org/0009-0003-8460-1574
citation:
ama: Bullerjahn N. Error estimates for full discretization by an almost mass conservation
technique for Cahn--Hilliard systems with dynamic boundary conditions. arXiv.
Published online 2025. doi:10.48550/ARXIV.2502.03847
apa: Bullerjahn, N. (2025). Error estimates for full discretization by an almost
mass conservation technique for Cahn--Hilliard systems with dynamic boundary conditions.
ArXiv. https://doi.org/10.48550/ARXIV.2502.03847
bibtex: '@article{Bullerjahn_2025, title={Error estimates for full discretization
by an almost mass conservation technique for Cahn--Hilliard systems with dynamic
boundary conditions}, DOI={10.48550/ARXIV.2502.03847},
journal={arXiv}, author={Bullerjahn, Nils}, year={2025} }'
chicago: Bullerjahn, Nils. “Error Estimates for Full Discretization by an Almost
Mass Conservation Technique for Cahn--Hilliard Systems with Dynamic Boundary Conditions.”
ArXiv, 2025. https://doi.org/10.48550/ARXIV.2502.03847.
ieee: 'N. Bullerjahn, “Error estimates for full discretization by an almost mass
conservation technique for Cahn--Hilliard systems with dynamic boundary conditions,”
arXiv, 2025, doi: 10.48550/ARXIV.2502.03847.'
mla: Bullerjahn, Nils. “Error Estimates for Full Discretization by an Almost Mass
Conservation Technique for Cahn--Hilliard Systems with Dynamic Boundary Conditions.”
ArXiv, 2025, doi:10.48550/ARXIV.2502.03847.
short: N. Bullerjahn, ArXiv (2025).
date_created: 2025-02-07T08:27:10Z
date_updated: 2025-02-07T08:28:48Z
department:
- _id: '841'
doi: 10.48550/ARXIV.2502.03847
language:
- iso: eng
publication: arXiv
status: public
title: Error estimates for full discretization by an almost mass conservation technique
for Cahn--Hilliard systems with dynamic boundary conditions
type: journal_article
user_id: '103797'
year: '2025'
...
---
_id: '58953'
abstract:
- lang: eng
text: In this article, we investigate symmetry properties of distributed systems
of mobile robots. We consider a swarm of n robots in the OBLOT model and analyze
their collective Fsync dynamics using of equivariant dynamical systems theory.
To this end, we show that the corresponding evolution function commutes with rotational
and reflective transformations of R^2. These form a group that is isomorphic to
O(2) x S_n, the product group of the orthogonal group and the permutation on n
elements. The theory of equivariant dynamical systems is used to deduce a hierarchy
along which symmetries of a robot swarm can potentially increase following an
arbitrary protocol. By decoupling the Look phase from the Compute and Move phases
in the mathematical description of an LCM cycle, this hierarchy can be characterized
in terms of automorphisms of connectivity graphs. In particular, we find all possible
types of symmetry increase, if the decoupled Compute and Move phase is invertible.
Finally, we apply our results to protocols which induce state-dependent linear
dynamics, where the reduced system consisting of only the Compute and Move phase
is linear.
author:
- first_name: Raphael
full_name: Gerlach, Raphael
id: '32655'
last_name: Gerlach
orcid: 0009-0002-4750-2051
- first_name: Sören
full_name: von der Gracht, Sören
id: '97359'
last_name: von der Gracht
orcid: 0000-0002-8054-2058
citation:
ama: Gerlach R, von der Gracht S. Analyzing Symmetries of Swarms of Mobile Robots
Using Equivariant Dynamical Systems. arXiv:250307576. Published online
2025.
apa: Gerlach, R., & von der Gracht, S. (2025). Analyzing Symmetries of Swarms
of Mobile Robots Using Equivariant Dynamical Systems. In arXiv:2503.07576.
bibtex: '@article{Gerlach_von der Gracht_2025, title={Analyzing Symmetries of Swarms
of Mobile Robots Using Equivariant Dynamical Systems}, journal={arXiv:2503.07576},
author={Gerlach, Raphael and von der Gracht, Sören}, year={2025} }'
chicago: Gerlach, Raphael, and Sören von der Gracht. “Analyzing Symmetries of Swarms
of Mobile Robots Using Equivariant Dynamical Systems.” ArXiv:2503.07576,
2025.
ieee: R. Gerlach and S. von der Gracht, “Analyzing Symmetries of Swarms of Mobile
Robots Using Equivariant Dynamical Systems,” arXiv:2503.07576. 2025.
mla: Gerlach, Raphael, and Sören von der Gracht. “Analyzing Symmetries of Swarms
of Mobile Robots Using Equivariant Dynamical Systems.” ArXiv:2503.07576,
2025.
short: R. Gerlach, S. von der Gracht, ArXiv:2503.07576 (2025).
date_created: 2025-03-11T08:21:05Z
date_updated: 2025-03-11T08:53:02Z
ddc:
- '004'
department:
- _id: '101'
external_id:
arxiv:
- '2503.07576'
file:
- access_level: open_access
content_type: application/pdf
creator: svdg
date_created: 2025-03-11T08:27:32Z
date_updated: 2025-03-11T08:27:32Z
file_id: '58954'
file_name: Analyzing_Symmetries_of_Swarms_of_Mobile_Robots_Using_Equivariant_Dynamical_Systems.pdf
file_size: 812198
relation: main_file
file_date_updated: 2025-03-11T08:27:32Z
has_accepted_license: '1'
keyword:
- dynamical systems
- coupled systems
- distributed computing
- robot swarms
- autonomous mobile robots
- symmetry
- equivariant dynamics
language:
- iso: eng
oa: '1'
page: '23'
project:
- _id: '106'
grant_number: '453112019'
name: 'Algorithmen für Schwarmrobotik: Verteiltes Rechnen trifft Dynamische Systeme'
publication: arXiv:2503.07576
status: public
title: Analyzing Symmetries of Swarms of Mobile Robots Using Equivariant Dynamical
Systems
type: preprint
user_id: '97359'
year: '2025'
...
---
_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. Journal of Complex Networks. 2024;12(2).
doi:10.1093/comnet/cnae009
apa: Bick, C., & von der Gracht, S. (2024). Heteroclinic dynamics in network
dynamical systems with higher-order interactions. Journal of Complex Networks,
12(2). https://doi.org/10.1093/comnet/cnae009
bibtex: '@article{Bick_von der Gracht_2024, title={Heteroclinic dynamics in network
dynamical systems with higher-order interactions}, volume={12}, DOI={10.1093/comnet/cnae009},
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.” Journal of Complex Networks
12, no. 2 (2024). https://doi.org/10.1093/comnet/cnae009.
ieee: 'C. Bick and S. von der Gracht, “Heteroclinic dynamics in network dynamical
systems with higher-order interactions,” Journal of Complex Networks, vol.
12, no. 2, 2024, doi: 10.1093/comnet/cnae009.'
mla: Bick, Christian, and Sören von der Gracht. “Heteroclinic Dynamics in Network
Dynamical Systems with Higher-Order Interactions.” Journal of Complex Networks,
vol. 12, no. 2, Oxford University Press (OUP), 2024, doi:10.1093/comnet/cnae009.
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'
...
---
_id: '45972'
author:
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
citation:
ama: Kovács B. Numerical surgery for mean curvature flow of surfaces. SIAM Journal
on Scientific Computing. 2024;46(2):A645--A669. doi:10.1137/22M1531919
apa: Kovács, B. (2024). Numerical surgery for mean curvature flow of surfaces. SIAM
Journal on Scientific Computing, 46(2), A645--A669. https://doi.org/10.1137/22M1531919
bibtex: '@article{Kovács_2024, title={Numerical surgery for mean curvature flow
of surfaces}, volume={46}, DOI={10.1137/22M1531919},
number={2}, journal={SIAM Journal on Scientific Computing}, author={Kovács, Balázs},
year={2024}, pages={A645--A669} }'
chicago: 'Kovács, Balázs. “Numerical Surgery for Mean Curvature Flow of Surfaces.”
SIAM Journal on Scientific Computing 46, no. 2 (2024): A645--A669. https://doi.org/10.1137/22M1531919.'
ieee: 'B. Kovács, “Numerical surgery for mean curvature flow of surfaces,” SIAM
Journal on Scientific Computing, vol. 46, no. 2, pp. A645--A669, 2024, doi:
10.1137/22M1531919.'
mla: Kovács, Balázs. “Numerical Surgery for Mean Curvature Flow of Surfaces.” SIAM
Journal on Scientific Computing, vol. 46, no. 2, 2024, pp. A645--A669, doi:10.1137/22M1531919.
short: B. Kovács, SIAM Journal on Scientific Computing 46 (2024) A645--A669.
date_created: 2023-07-10T12:32:34Z
date_updated: 2024-08-27T07:42:56Z
department:
- _id: '841'
doi: 10.1137/22M1531919
extern: '1'
intvolume: ' 46'
issue: '2'
language:
- iso: eng
page: A645--A669
publication: SIAM Journal on Scientific Computing
status: public
title: Numerical surgery for mean curvature flow of surfaces
type: journal_article
user_id: '100441'
volume: 46
year: '2024'
...
---
_id: '55078'
abstract:
- lang: eng
text: "This paper develops and discusses a residual-based a posteriori error\r\nestimate
and a space--time adaptive algorithm for solving parabolic surface\r\npartial
differential equations on closed stationary surfaces. The full\r\ndiscretization
uses the surface finite element method in space and the backward\r\nEuler method
in time. The proposed error indicator bounds the error quantities\r\nglobally
in space from above and below, and globally in time from above and\r\nlocally
from below. A space--time adaptive algorithm is proposed using the\r\nderived
error indicator. Numerical experiments illustrate and complement the\r\ntheory."
author:
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
- first_name: Michael Frederik Raúl
full_name: Lantelme, Michael Frederik Raúl
id: '102867'
last_name: Lantelme
citation:
ama: Kovács B, Lantelme MFR. A posteriori error estimates for parabolic partial
differential equations on stationary surfaces. arXiv:240702101. Published
online 2024.
apa: Kovács, B., & Lantelme, M. F. R. (2024). A posteriori error estimates for
parabolic partial differential equations on stationary surfaces. In arXiv:2407.02101.
bibtex: '@article{Kovács_Lantelme_2024, title={A posteriori error estimates for
parabolic partial differential equations on stationary surfaces}, journal={arXiv:2407.02101},
author={Kovács, Balázs and Lantelme, Michael Frederik Raúl}, year={2024} }'
chicago: Kovács, Balázs, and Michael Frederik Raúl Lantelme. “A Posteriori Error
Estimates for Parabolic Partial Differential Equations on Stationary Surfaces.”
ArXiv:2407.02101, 2024.
ieee: B. Kovács and M. F. R. Lantelme, “A posteriori error estimates for parabolic
partial differential equations on stationary surfaces,” arXiv:2407.02101.
2024.
mla: Kovács, Balázs, and Michael Frederik Raúl Lantelme. “A Posteriori Error Estimates
for Parabolic Partial Differential Equations on Stationary Surfaces.” ArXiv:2407.02101,
2024.
short: B. Kovács, M.F.R. Lantelme, ArXiv:2407.02101 (2024).
date_created: 2024-07-04T12:53:47Z
date_updated: 2026-02-18T14:45:36Z
department:
- _id: '841'
external_id:
arxiv:
- '2407.02101'
language:
- iso: eng
publication: arXiv:2407.02101
status: public
title: A posteriori error estimates for parabolic partial differential equations on
stationary surfaces
type: preprint
user_id: '100441'
year: '2024'
...
---
_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. Proceedings of the Royal Society A: Mathematical, Physical
and Engineering Sciences. 2024;480(2301). doi:10.1098/rspa.2023.0945'
apa: 'von der Gracht, S., Nijholt, E., & Rink, B. (2024). Higher-order interactions
lead to ‘reluctant’ synchrony breaking. Proceedings of the Royal Society A:
Mathematical, Physical and Engineering Sciences, 480(2301). https://doi.org/10.1098/rspa.2023.0945'
bibtex: '@article{von der Gracht_Nijholt_Rink_2024, title={Higher-order interactions
lead to ‘reluctant’ synchrony breaking}, volume={480}, DOI={10.1098/rspa.2023.0945},
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.” Proceedings of the Royal Society A:
Mathematical, Physical and Engineering Sciences 480, no. 2301 (2024). https://doi.org/10.1098/rspa.2023.0945.'
ieee: 'S. von der Gracht, E. Nijholt, and B. Rink, “Higher-order interactions lead
to ‘reluctant’ synchrony breaking,” Proceedings of the Royal Society A: Mathematical,
Physical and Engineering Sciences, vol. 480, no. 2301, 2024, doi: 10.1098/rspa.2023.0945.'
mla: 'von der Gracht, Sören, et al. “Higher-Order Interactions Lead to ‘Reluctant’
Synchrony Breaking.” Proceedings of the Royal Society A: Mathematical, Physical
and Engineering Sciences, vol. 480, no. 2301, The Royal Society, 2024, doi:10.1098/rspa.2023.0945.'
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'
...
---
_id: '49326'
abstract:
- lang: eng
text: 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.
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. Hypernetworks: Cluster Synchronization
Is a Higher-Order Effect. SIAM Journal on Applied Mathematics. 2023;83(6):2329-2353.
doi:10.1137/23m1561075'
apa: 'von der Gracht, S., Nijholt, E., & Rink, B. (2023). Hypernetworks: Cluster
Synchronization Is a Higher-Order Effect. SIAM Journal on Applied Mathematics,
83(6), 2329–2353. https://doi.org/10.1137/23m1561075'
bibtex: '@article{von der Gracht_Nijholt_Rink_2023, title={Hypernetworks: Cluster
Synchronization Is a Higher-Order Effect}, volume={83}, DOI={10.1137/23m1561075},
number={6}, journal={SIAM Journal on Applied Mathematics}, publisher={Society
for Industrial & Applied Mathematics (SIAM)}, author={von der Gracht, Sören
and Nijholt, Eddie and Rink, Bob}, year={2023}, pages={2329–2353} }'
chicago: 'Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “Hypernetworks: Cluster
Synchronization Is a Higher-Order Effect.” SIAM Journal on Applied Mathematics
83, no. 6 (2023): 2329–53. https://doi.org/10.1137/23m1561075.'
ieee: 'S. von der Gracht, E. Nijholt, and B. Rink, “Hypernetworks: Cluster Synchronization
Is a Higher-Order Effect,” SIAM Journal on Applied Mathematics, vol. 83,
no. 6, pp. 2329–2353, 2023, doi: 10.1137/23m1561075.'
mla: 'von der Gracht, Sören, et al. “Hypernetworks: Cluster Synchronization Is a
Higher-Order Effect.” SIAM Journal on Applied Mathematics, vol. 83, no.
6, Society for Industrial & Applied Mathematics (SIAM), 2023, pp. 2329–53,
doi:10.1137/23m1561075.'
short: S. von der Gracht, E. Nijholt, B. Rink, SIAM Journal on Applied Mathematics
83 (2023) 2329–2353.
date_created: 2023-11-29T10:50:05Z
date_updated: 2023-11-29T10:52:23Z
department:
- _id: '101'
doi: 10.1137/23m1561075
external_id:
arxiv:
- '2302.08974'
intvolume: ' 83'
issue: '6'
keyword:
- Applied Mathematics
language:
- iso: eng
page: 2329-2353
publication: SIAM Journal on Applied Mathematics
publication_identifier:
issn:
- 0036-1399
- 1095-712X
publication_status: published
publisher: Society for Industrial & Applied Mathematics (SIAM)
status: public
title: 'Hypernetworks: Cluster Synchronization Is a Higher-Order Effect'
type: journal_article
user_id: '97359'
volume: 83
year: '2023'
...
---
_id: '45971'
abstract:
- lang: eng
text: "Abstract\r\n An error estimate
for a canonical discretization of the harmonic map heat flow into spheres is derived.
The numerical scheme uses standard finite elements with a nodal treatment of linearized
unit-length constraints. The analysis is based on elementary approximation results
and only uses the discrete weak formulation."
author:
- first_name: Sören
full_name: Bartels, Sören
last_name: Bartels
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
- first_name: Zhangxian
full_name: Wang, Zhangxian
last_name: Wang
citation:
ama: Bartels S, Kovács B, Wang Z. Error analysis for the numerical approximation
of the harmonic map heat flow with nodal constraints. IMA Journal of Numerical
Analysis. Published online 2023. doi:10.1093/imanum/drad037
apa: Bartels, S., Kovács, B., & Wang, Z. (2023). Error analysis for the numerical
approximation of the harmonic map heat flow with nodal constraints. IMA Journal
of Numerical Analysis. https://doi.org/10.1093/imanum/drad037
bibtex: '@article{Bartels_Kovács_Wang_2023, title={Error analysis for the numerical
approximation of the harmonic map heat flow with nodal constraints}, DOI={10.1093/imanum/drad037},
journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press
(OUP)}, author={Bartels, Sören and Kovács, Balázs and Wang, Zhangxian}, year={2023}
}'
chicago: Bartels, Sören, Balázs Kovács, and Zhangxian Wang. “Error Analysis for
the Numerical Approximation of the Harmonic Map Heat Flow with Nodal Constraints.”
IMA Journal of Numerical Analysis, 2023. https://doi.org/10.1093/imanum/drad037.
ieee: 'S. Bartels, B. Kovács, and Z. Wang, “Error analysis for the numerical approximation
of the harmonic map heat flow with nodal constraints,” IMA Journal of Numerical
Analysis, 2023, doi: 10.1093/imanum/drad037.'
mla: Bartels, Sören, et al. “Error Analysis for the Numerical Approximation of the
Harmonic Map Heat Flow with Nodal Constraints.” IMA Journal of Numerical Analysis,
Oxford University Press (OUP), 2023, doi:10.1093/imanum/drad037.
short: S. Bartels, B. Kovács, Z. Wang, IMA Journal of Numerical Analysis (2023).
date_created: 2023-07-10T12:32:10Z
date_updated: 2024-04-03T09:15:27Z
department:
- _id: '841'
doi: 10.1093/imanum/drad037
keyword:
- Applied Mathematics
- Computational Mathematics
- General Mathematics
language:
- iso: eng
publication: IMA Journal of Numerical Analysis
publication_identifier:
issn:
- 0272-4979
- 1464-3642
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Error analysis for the numerical approximation of the harmonic map heat flow
with nodal constraints
type: journal_article
user_id: '100441'
year: '2023'
...
---
_id: '53140'
abstract:
- lang: eng
text: We present a new stability and error analysis of fully discrete approximation
schemes for the transient Stokes equation. For the spatial discretization, we
consider a wide class of Galerkin finite element methods which includes both inf-sup
stable spaces and symmetric pressure stabilized formulations. We extend the results
from Burman and Fernández [\textit{SIAM J. Numer. Anal.}, 47 (2009), pp. 409-439]
and provide a unified theoretical analysis of backward difference formulae (BDF
methods) of order 1 to 6. The main novelty of our approach lies in the use of
Dahlquist's G-stability concept together with multiplier techniques introduced
by Nevannlina-Odeh and recently by Akrivis et al. [\textit{SIAM J. Numer. Anal.},
59 (2021), pp. 2449-2472] to derive optimal stability and error estimates for
both the velocity and the pressure. When combined with a method dependent Ritz
projection for the initial data, unconditional stability can be shown while for
arbitrary interpolation, pressure stability is subordinate to the fulfillment
of a mild inverse CFL-type condition between space and time discretizations.
author:
- first_name: Alessandro
full_name: Contri, Alessandro
last_name: Contri
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
- first_name: André
full_name: Massing, André
last_name: Massing
citation:
ama: 'Contri A, Kovács B, Massing A. Error analysis of BDF 1-6 time-stepping methods
for the transient Stokes problem: velocity and pressure estimates. arXiv.
Published online 2023. doi:10.48550/ARXIV.2312.05511'
apa: 'Contri, A., Kovács, B., & Massing, A. (2023). Error analysis of BDF 1-6
time-stepping methods for the transient Stokes problem: velocity and pressure
estimates. ArXiv. https://doi.org/10.48550/ARXIV.2312.05511'
bibtex: '@article{Contri_Kovács_Massing_2023, title={Error analysis of BDF 1-6 time-stepping
methods for the transient Stokes problem: velocity and pressure estimates}, DOI={10.48550/ARXIV.2312.05511},
journal={arXiv}, author={Contri, Alessandro and Kovács, Balázs and Massing, André},
year={2023} }'
chicago: 'Contri, Alessandro, Balázs Kovács, and André Massing. “Error Analysis
of BDF 1-6 Time-Stepping Methods for the Transient Stokes Problem: Velocity and
Pressure Estimates.” ArXiv, 2023. https://doi.org/10.48550/ARXIV.2312.05511.'
ieee: 'A. Contri, B. Kovács, and A. Massing, “Error analysis of BDF 1-6 time-stepping
methods for the transient Stokes problem: velocity and pressure estimates,” arXiv,
2023, doi: 10.48550/ARXIV.2312.05511.'
mla: 'Contri, Alessandro, et al. “Error Analysis of BDF 1-6 Time-Stepping Methods
for the Transient Stokes Problem: Velocity and Pressure Estimates.” ArXiv,
2023, doi:10.48550/ARXIV.2312.05511.'
short: A. Contri, B. Kovács, A. Massing, ArXiv (2023).
date_created: 2024-04-03T09:08:38Z
date_updated: 2024-04-03T09:12:47Z
department:
- _id: '841'
doi: 10.48550/ARXIV.2312.05511
language:
- iso: eng
publication: arXiv
status: public
title: 'Error analysis of BDF 1-6 time-stepping methods for the transient Stokes problem:
velocity and pressure estimates'
type: journal_article
user_id: '100441'
year: '2023'
...
---
_id: '45498'
abstract:
- lang: eng
text: "We present a novel method for high-order phase reduction in networks of\r\nweakly
coupled oscillators and, more generally, perturbations of reducible\r\nnormally
hyperbolic (quasi-)periodic tori. Our method works by computing an\r\nasymptotic
expansion for an embedding of the perturbed invariant torus, as well\r\nas for
the reduced phase dynamics in local coordinates. Both can be determined\r\nto
arbitrary degrees of accuracy, and we show that the phase dynamics may\r\ndirectly
be obtained in normal form. We apply the method to predict remote\r\nsynchronisation
in a chain of coupled Stuart-Landau oscillators."
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. A parametrisation method for high-order
phase reduction in coupled oscillator networks. arXiv:230603320.
apa: von der Gracht, S., Nijholt, E., & Rink, B. (n.d.). A parametrisation method
for high-order phase reduction in coupled oscillator networks. In arXiv:2306.03320.
bibtex: '@article{von der Gracht_Nijholt_Rink, title={A parametrisation method for
high-order phase reduction in coupled oscillator networks}, journal={arXiv:2306.03320},
author={von der Gracht, Sören and Nijholt, Eddie and Rink, Bob} }'
chicago: Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “A Parametrisation
Method for High-Order Phase Reduction in Coupled Oscillator Networks.” ArXiv:2306.03320,
n.d.
ieee: S. von der Gracht, E. Nijholt, and B. Rink, “A parametrisation method for
high-order phase reduction in coupled oscillator networks,” arXiv:2306.03320.
.
mla: von der Gracht, Sören, et al. “A Parametrisation Method for High-Order Phase
Reduction in Coupled Oscillator Networks.” ArXiv:2306.03320.
short: S. von der Gracht, E. Nijholt, B. Rink, ArXiv:2306.03320 (n.d.).
date_created: 2023-06-07T07:57:28Z
date_updated: 2023-06-07T07:59:06Z
department:
- _id: '101'
external_id:
arxiv:
- '2306.03320'
language:
- iso: eng
main_file_link:
- url: https://arxiv.org/pdf/2306.03320
page: '29'
publication: arXiv:2306.03320
publication_status: submitted
status: public
title: A parametrisation method for high-order phase reduction in coupled oscillator
networks
type: preprint
user_id: '97359'
year: '2023'
...
---
_id: '33264'
abstract:
- lang: eng
text: We investigate bifurcations in feedforward coupled cell networks. Feedforward
structure (the absence of feedback) can be defined by a partial order on the cells.
We use this property to study generic one-parameter steady state bifurcations
for such networks. Branching solutions and their asymptotics are described in
terms of Taylor coefficients of the internal dynamics. They can be determined
via an algorithm that only exploits the network structure. Similar to previous
results on feedforward chains, we observe amplifications of the growth rates of
steady state branches induced by the feedforward structure. However, contrary
to these earlier results, as the interaction scenarios can be more complicated
in general feedforward networks, different branching patterns and different amplifications
can occur for different regions in the space of Taylor coefficients.
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. Amplified steady state bifurcations in
feedforward networks. Nonlinearity. 2022;35(4):2073-2120. doi:10.1088/1361-6544/ac5463
apa: von der Gracht, S., Nijholt, E., & Rink, B. (2022). Amplified steady state
bifurcations in feedforward networks. Nonlinearity, 35(4), 2073–2120.
https://doi.org/10.1088/1361-6544/ac5463
bibtex: '@article{von der Gracht_Nijholt_Rink_2022, title={Amplified steady state
bifurcations in feedforward networks}, volume={35}, DOI={10.1088/1361-6544/ac5463},
number={4}, journal={Nonlinearity}, publisher={IOP Publishing}, author={von der
Gracht, Sören and Nijholt, Eddie and Rink, Bob}, year={2022}, pages={2073–2120}
}'
chicago: 'Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “Amplified Steady
State Bifurcations in Feedforward Networks.” Nonlinearity 35, no. 4 (2022):
2073–2120. https://doi.org/10.1088/1361-6544/ac5463.'
ieee: 'S. von der Gracht, E. Nijholt, and B. Rink, “Amplified steady state bifurcations
in feedforward networks,” Nonlinearity, vol. 35, no. 4, pp. 2073–2120,
2022, doi: 10.1088/1361-6544/ac5463.'
mla: von der Gracht, Sören, et al. “Amplified Steady State Bifurcations in Feedforward
Networks.” Nonlinearity, vol. 35, no. 4, IOP Publishing, 2022, pp. 2073–120,
doi:10.1088/1361-6544/ac5463.
short: S. von der Gracht, E. Nijholt, B. Rink, Nonlinearity 35 (2022) 2073–2120.
date_created: 2022-09-06T11:38:15Z
date_updated: 2022-09-07T08:36:46Z
doi: 10.1088/1361-6544/ac5463
extern: '1'
external_id:
arxiv:
- '2105.02547'
intvolume: ' 35'
issue: '4'
keyword:
- Applied Mathematics
- General Physics and Astronomy
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
page: 2073-2120
publication: Nonlinearity
publication_identifier:
issn:
- 0951-7715
- 1361-6544
publication_status: published
publisher: IOP Publishing
status: public
title: Amplified steady state bifurcations in feedforward networks
type: journal_article
user_id: '97359'
volume: 35
year: '2022'
...
---
_id: '45970'
abstract:
- lang: eng
text: ' We introduce a new phase field model for tumor growth where viscoelastic
effects are taken into account. The model is derived from basic thermodynamical
principles and consists of a convected Cahn–Hilliard equation with source terms
for the tumor cells and a convected reaction–diffusion equation with boundary
supply for the nutrient. Chemotactic terms, which are essential for the invasive
behavior of tumors, are taken into account. The model is completed by a viscoelastic
system consisting of the Navier–Stokes equation for the hydrodynamic quantities,
and a general constitutive equation with stress relaxation for the left Cauchy–Green
tensor associated with the elastic part of the total mechanical response of the
viscoelastic material. For a specific choice of the elastic energy density and
with an additional dissipative term accounting for stress diffusion, we prove
existence of global-in-time weak solutions of the viscoelastic model for tumor
growth in two space dimensions [Formula: see text] by the passage to the limit
in a fully-discrete finite element scheme where a CFL condition, i.e. [Formula:
see text], is required. Moreover, in arbitrary dimensions [Formula:
see text], we show stability and existence of solutions for the fully-discrete
finite element scheme, where positive definiteness of the discrete Cauchy–Green
tensor is proved with a regularization technique that was first introduced by
Barrett and Boyaval [Existence and approximation of a (regularized) Oldroyd-B
model, Math. Models Methods Appl. Sci. 21 (2011) 1783–1837]. After that, we improve
the regularity results in arbitrary dimensions [Formula: see text] and in two
dimensions [Formula: see text], where a CFL condition is required. Then, in two
dimensions [Formula: see text], we pass to the limit in the discretization parameters
and show that subsequences of discrete solutions converge to a global-in-time
weak solution. Finally, we present numerical results in two dimensions [Formula:
see text]. '
author:
- first_name: Harald
full_name: Garcke, Harald
last_name: Garcke
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
- first_name: Dennis
full_name: Trautwein, Dennis
last_name: Trautwein
citation:
ama: Garcke H, Kovács B, Trautwein D. Viscoelastic Cahn–Hilliard models for tumor
growth. Mathematical Models and Methods in Applied Sciences. 2022;32(13):2673-2758.
doi:10.1142/s0218202522500634
apa: Garcke, H., Kovács, B., & Trautwein, D. (2022). Viscoelastic Cahn–Hilliard
models for tumor growth. Mathematical Models and Methods in Applied Sciences,
32(13), 2673–2758. https://doi.org/10.1142/s0218202522500634
bibtex: '@article{Garcke_Kovács_Trautwein_2022, title={Viscoelastic Cahn–Hilliard
models for tumor growth}, volume={32}, DOI={10.1142/s0218202522500634},
number={13}, journal={Mathematical Models and Methods in Applied Sciences}, publisher={World
Scientific Pub Co Pte Ltd}, author={Garcke, Harald and Kovács, Balázs and Trautwein,
Dennis}, year={2022}, pages={2673–2758} }'
chicago: 'Garcke, Harald, Balázs Kovács, and Dennis Trautwein. “Viscoelastic Cahn–Hilliard
Models for Tumor Growth.” Mathematical Models and Methods in Applied Sciences
32, no. 13 (2022): 2673–2758. https://doi.org/10.1142/s0218202522500634.'
ieee: 'H. Garcke, B. Kovács, and D. Trautwein, “Viscoelastic Cahn–Hilliard models
for tumor growth,” Mathematical Models and Methods in Applied Sciences,
vol. 32, no. 13, pp. 2673–2758, 2022, doi: 10.1142/s0218202522500634.'
mla: Garcke, Harald, et al. “Viscoelastic Cahn–Hilliard Models for Tumor Growth.”
Mathematical Models and Methods in Applied Sciences, vol. 32, no. 13, World
Scientific Pub Co Pte Ltd, 2022, pp. 2673–758, doi:10.1142/s0218202522500634.
short: H. Garcke, B. Kovács, D. Trautwein, Mathematical Models and Methods in Applied
Sciences 32 (2022) 2673–2758.
date_created: 2023-07-10T11:47:27Z
date_updated: 2024-04-03T09:15:35Z
department:
- _id: '841'
doi: 10.1142/s0218202522500634
intvolume: ' 32'
issue: '13'
keyword:
- Applied Mathematics
- Modeling and Simulation
language:
- iso: eng
page: 2673-2758
publication: Mathematical Models and Methods in Applied Sciences
publication_identifier:
issn:
- 0218-2025
- 1793-6314
publication_status: published
publisher: World Scientific Pub Co Pte Ltd
status: public
title: Viscoelastic Cahn–Hilliard models for tumor growth
type: journal_article
user_id: '100441'
volume: 32
year: '2022'
...