Network dynamics with higher-order interactions: coupled cell hypernetworks for identical cells and synchrony

Manuela Aguiar; Christian Bick; Ana Dias

doi:10.1088/1361-6544/ace39f

Network dynamics with higher-order interactions: coupled cell hypernetworks for identical cells and synchrony

Manuela Aguiar, Christian Bick^*, Ana Dias

^*Corresponding author for this work

Research output: Contribution to Journal › Article › Academic › peer-review

Abstract

Network interactions that are nonlinear in the state of more than two nodes—also known as higher-order interactions—can have a profound impact on the collective network dynamics. Here we develop a coupled cell hypernetwork formalism to elucidate the existence and stability of (cluster) synchronization patterns in network dynamical systems with higher-order interactions. More specifically, we define robust synchrony subspace for coupled cell hypernetworks whose coupling structure is determined by an underlying hypergraph and describe those spaces for general such hypernetworks. Since a hypergraph can be equivalently represented as a bipartite graph between its nodes and hyperedges, we relate the synchrony subspaces of a hypernetwork to balanced colourings of the corresponding incidence digraph.

Original language	English
Pages (from-to)	4641-4673
Number of pages	33
Journal	Nonlinearity
Volume	36
Issue number	9
Early online date	24 Jul 2023
DOIs	https://doi.org/10.1088/1361-6544/ace39f
Publication status	Published - Sept 2023

Bibliographical note

Funding Information:
M A and A D were partially supported by CMUP, member of LASI, which is financed by national funds through FCT – Fundação para a Ciência e a Tecnologia, I.P., under the projects with reference UIDB/00144/2020 and UIDP/00144/2020. C B acknowledges support from the Engineering and Physical Sciences Research Council (EPSRC) through the Grant EP/T013613/1.

Publisher Copyright:
© 2023 IOP Publishing Ltd & London Mathematical Society

Funding

M A and A D were partially supported by CMUP, member of LASI, which is financed by national funds through FCT – Fundação para a Ciência e a Tecnologia, I.P., under the projects with reference UIDB/00144/2020 and UIDP/00144/2020. C B acknowledges support from the Engineering and Physical Sciences Research Council (EPSRC) through the Grant EP/T013613/1.

Keywords

34C15
34D06
37C99
37Nxx
coupled cell networks
higher-order interactions
hypergraphs
network dynamical systems
synchronization

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10.1088/1361-6544/ace39f

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title = "Network dynamics with higher-order interactions: coupled cell hypernetworks for identical cells and synchrony",

abstract = "Network interactions that are nonlinear in the state of more than two nodes—also known as higher-order interactions—can have a profound impact on the collective network dynamics. Here we develop a coupled cell hypernetwork formalism to elucidate the existence and stability of (cluster) synchronization patterns in network dynamical systems with higher-order interactions. More specifically, we define robust synchrony subspace for coupled cell hypernetworks whose coupling structure is determined by an underlying hypergraph and describe those spaces for general such hypernetworks. Since a hypergraph can be equivalently represented as a bipartite graph between its nodes and hyperedges, we relate the synchrony subspaces of a hypernetwork to balanced colourings of the corresponding incidence digraph.",

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author = "Manuela Aguiar and Christian Bick and Ana Dias",

note = "Funding Information: M A and A D were partially supported by CMUP, member of LASI, which is financed by national funds through FCT – Funda{\c c}{\~a}o para a Ci{\^e}ncia e a Tecnologia, I.P., under the projects with reference UIDB/00144/2020 and UIDP/00144/2020. C B acknowledges support from the Engineering and Physical Sciences Research Council (EPSRC) through the Grant EP/T013613/1. Publisher Copyright: {\textcopyright} 2023 IOP Publishing Ltd \& London Mathematical Society",

year = "2023",

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doi = "10.1088/1361-6544/ace39f",

language = "English",

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T2 - coupled cell hypernetworks for identical cells and synchrony

AU - Aguiar, Manuela

AU - Bick, Christian

AU - Dias, Ana

N1 - Funding Information: M A and A D were partially supported by CMUP, member of LASI, which is financed by national funds through FCT – Fundação para a Ciência e a Tecnologia, I.P., under the projects with reference UIDB/00144/2020 and UIDP/00144/2020. C B acknowledges support from the Engineering and Physical Sciences Research Council (EPSRC) through the Grant EP/T013613/1. Publisher Copyright: © 2023 IOP Publishing Ltd & London Mathematical Society

PY - 2023/9

Y1 - 2023/9

N2 - Network interactions that are nonlinear in the state of more than two nodes—also known as higher-order interactions—can have a profound impact on the collective network dynamics. Here we develop a coupled cell hypernetwork formalism to elucidate the existence and stability of (cluster) synchronization patterns in network dynamical systems with higher-order interactions. More specifically, we define robust synchrony subspace for coupled cell hypernetworks whose coupling structure is determined by an underlying hypergraph and describe those spaces for general such hypernetworks. Since a hypergraph can be equivalently represented as a bipartite graph between its nodes and hyperedges, we relate the synchrony subspaces of a hypernetwork to balanced colourings of the corresponding incidence digraph.

AB - Network interactions that are nonlinear in the state of more than two nodes—also known as higher-order interactions—can have a profound impact on the collective network dynamics. Here we develop a coupled cell hypernetwork formalism to elucidate the existence and stability of (cluster) synchronization patterns in network dynamical systems with higher-order interactions. More specifically, we define robust synchrony subspace for coupled cell hypernetworks whose coupling structure is determined by an underlying hypergraph and describe those spaces for general such hypernetworks. Since a hypergraph can be equivalently represented as a bipartite graph between its nodes and hyperedges, we relate the synchrony subspaces of a hypernetwork to balanced colourings of the corresponding incidence digraph.

KW - 34C15

KW - 34D06

KW - 37C99

KW - 37Nxx

KW - coupled cell networks

KW - higher-order interactions

KW - hypergraphs

KW - network dynamical systems

KW - synchronization

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SN - 0951-7715

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SP - 4641

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JO - Nonlinearity

JF - Nonlinearity

IS - 9

ER -

Network dynamics with higher-order interactions: coupled cell hypernetworks for identical cells and synchrony

Abstract

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Keywords

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