The transition to synchronization of networked systems
The transition to synchronization of networked systems
We study the synchronization properties of a generic networked dynamical system, and show that, under a suitable approximation, the transition to synchronization can be predicted with the only help of eigenvalues and eigenvectors of the graph Laplacian matrix. The transition comes out to be made of a well defined sequence of events, each of which corresponds to a specific clustered state. The network’s nodes involved in each of the clusters can be identified, and the value of the coupling strength at which the events are taking place can be approximately ascertained. Finally, we present large-scale simulations which show the accuracy of the approximation made, and of our predictions in describing the synchronization transition of both synthetic and real-world large size networks, and we even report that the observed sequence of clusters is preserved in heterogeneous networks made of slightly non-identical systems.
Bayani, Atiyeh
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Nazarimehr, Fahimeh
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Jafari, Sajad
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Kovalenko, Kirill
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Contreras-Aso, Gonzalo
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Alfaro-Bittner, Karin
f94137b4-6ec7-4266-b2f0-8773623a55df
Sanchez-Garcia, Ruben J.
8246cea2-ae1c-44f2-94e9-bacc9371c3ed
Boccaletti, Stefano
53b7ff00-13bf-435c-99ef-38ffa67c596a
10 June 2024
Bayani, Atiyeh
9247d769-4979-43db-924c-dee1d71345d9
Nazarimehr, Fahimeh
690afd91-8189-410d-b446-6cf2026d9a5a
Jafari, Sajad
79deecd5-48bb-45ee-828d-b7c2cd93acb3
Kovalenko, Kirill
fb055851-da87-4408-96fe-e714174d171e
Contreras-Aso, Gonzalo
272c853d-0720-4cce-8b09-cc41c3ba19f0
Alfaro-Bittner, Karin
f94137b4-6ec7-4266-b2f0-8773623a55df
Sanchez-Garcia, Ruben J.
8246cea2-ae1c-44f2-94e9-bacc9371c3ed
Boccaletti, Stefano
53b7ff00-13bf-435c-99ef-38ffa67c596a
Bayani, Atiyeh, Nazarimehr, Fahimeh, Jafari, Sajad, Kovalenko, Kirill, Contreras-Aso, Gonzalo, Alfaro-Bittner, Karin, Sanchez-Garcia, Ruben J. and Boccaletti, Stefano
(2024)
The transition to synchronization of networked systems.
Nature Communications, 15 (1), [4955].
(doi:10.1038/s41467-024-48203-6).
Abstract
We study the synchronization properties of a generic networked dynamical system, and show that, under a suitable approximation, the transition to synchronization can be predicted with the only help of eigenvalues and eigenvectors of the graph Laplacian matrix. The transition comes out to be made of a well defined sequence of events, each of which corresponds to a specific clustered state. The network’s nodes involved in each of the clusters can be identified, and the value of the coupling strength at which the events are taking place can be approximately ascertained. Finally, we present large-scale simulations which show the accuracy of the approximation made, and of our predictions in describing the synchronization transition of both synthetic and real-world large size networks, and we even report that the observed sequence of clusters is preserved in heterogeneous networks made of slightly non-identical systems.
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Accepted/In Press date: 23 April 2024
Published date: 10 June 2024
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© The Author(s) 2024.
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Local EPrints ID: 489532
URI: http://eprints.soton.ac.uk/id/eprint/489532
ISSN: 2041-1723
PURE UUID: 3ec975a5-03f5-43fe-826e-f4a3618851dc
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Date deposited: 26 Apr 2024 16:46
Last modified: 12 Jul 2024 01:47
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Contributors
Author:
Atiyeh Bayani
Author:
Fahimeh Nazarimehr
Author:
Sajad Jafari
Author:
Kirill Kovalenko
Author:
Gonzalo Contreras-Aso
Author:
Karin Alfaro-Bittner
Author:
Stefano Boccaletti
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