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Coupled hypergraph maps and chaotic cluster synchronization

Coupled hypergraph maps and chaotic cluster synchronization
Coupled hypergraph maps and chaotic cluster synchronization
Coupled map lattices (CMLs) are prototypical dynamical systems on networks/graphs. They exhibit complex patterns generated via the interplay of diffusive/Laplacian coupling and nonlinear reactions modelled by a single iterated map at each node; the maps are often taken as unimodal, e.g., logistic or tent maps. In this letter, we propose a class of higher-order coupled dynamical systems involving the hypergraph Laplacian, which we call coupled hypergraph maps (CHMs). By combining linearized (in-)stability analysis of synchronized states, hypergraph spectral theory, and numerical methods, we detect robust regions of chaotic cluster synchronization occurring in parameter space upon varying coupling strength and the main bifurcation parameter of the unimodal map. Furthermore, we find key differences between Laplacian and hypergraph Laplacian coupling and detect various other classes of periodic and quasi-periodic patterns. The results show the high complexity of coupled graph maps and indicate that they might be an excellent universal model class to understand the similarities and differences between dynamics on classical graphs and dynamics on hypergraphs.
0295-5075
Böhle, Tobias
80fa0494-b7e0-45f6-8b5e-800b1538695d
Kuehn, Christian
5d5248f6-c34e-47bd-bd1b-519bd8cb1ae8
Mulas, Raffaella
1ceeaad9-da27-4bb3-bd5b-4f0c7ec422e5
Jost, Jürgen
a176b589-d079-48f8-ad45-1359cfdc153d
Böhle, Tobias
80fa0494-b7e0-45f6-8b5e-800b1538695d
Kuehn, Christian
5d5248f6-c34e-47bd-bd1b-519bd8cb1ae8
Mulas, Raffaella
1ceeaad9-da27-4bb3-bd5b-4f0c7ec422e5
Jost, Jürgen
a176b589-d079-48f8-ad45-1359cfdc153d

Böhle, Tobias, Kuehn, Christian, Mulas, Raffaella and Jost, Jürgen (2022) Coupled hypergraph maps and chaotic cluster synchronization. Europhysics Letters, 136 (4), [40005]. (doi:10.1209/0295-5075/ac1a26).

Record type: Article

Abstract

Coupled map lattices (CMLs) are prototypical dynamical systems on networks/graphs. They exhibit complex patterns generated via the interplay of diffusive/Laplacian coupling and nonlinear reactions modelled by a single iterated map at each node; the maps are often taken as unimodal, e.g., logistic or tent maps. In this letter, we propose a class of higher-order coupled dynamical systems involving the hypergraph Laplacian, which we call coupled hypergraph maps (CHMs). By combining linearized (in-)stability analysis of synchronized states, hypergraph spectral theory, and numerical methods, we detect robust regions of chaotic cluster synchronization occurring in parameter space upon varying coupling strength and the main bifurcation parameter of the unimodal map. Furthermore, we find key differences between Laplacian and hypergraph Laplacian coupling and detect various other classes of periodic and quasi-periodic patterns. The results show the high complexity of coupled graph maps and indicate that they might be an excellent universal model class to understand the similarities and differences between dynamics on classical graphs and dynamics on hypergraphs.

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Coupled Hypergraph Maps and Chaotic Cluster Synchronization - Accepted Manuscript
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Accepted/In Press date: 3 August 2021
e-pub ahead of print date: 10 March 2022
Additional Information: Funding Information: The authors thank two anonymous referees whose comments helped to improve the paper. TB thanks the TUM Institute for Advanced Study (TUM-IAS) for support through a Hans Fischer Fellowship awarded to Chris Bick . TB also acknowledges support of the TUM TopMath elite study program. CK was supported a Lichtenberg Professorship of the VolkswagenStiftung. RM was supported by The Alan Turing Institute under the EPSRC grant EP/N510129/1. JJ was partially supported by GIF grant No. I-1514-304.6/2019. Publisher Copyright: Copyright © 2022 EPLA. Copyright: Copyright 2022 Elsevier B.V., All rights reserved.

Identifiers

Local EPrints ID: 456861
URI: http://eprints.soton.ac.uk/id/eprint/456861
ISSN: 0295-5075
PURE UUID: 4c8b476c-156b-4bcd-8788-4ce96737a8a6

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Date deposited: 13 May 2022 16:37
Last modified: 03 Aug 2022 04:01

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Contributors

Author: Tobias Böhle
Author: Christian Kuehn
Author: Raffaella Mulas
Author: Jürgen Jost

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