Mean-field nature of synchronization stability in networks with multiple interaction layers

Charo del Genio; Sergio Faci-Lázaro; Jesús Gómez-Gardeñes; Stefano Boccaletti

doi:10.1038/s42005-022-00897-0

Mean-field nature of synchronization stability in networks with multiple interaction layers

Charo del Genio, Sergio Faci-Lázaro, Jesús Gómez-Gardeñes, Stefano Boccaletti

Research Centre for Fluid and Complex Systems

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

59 Downloads (Pure)

Abstract

The interactions between the components of many real-world systems are best modelled by networks with multiple layers. Different theories have been proposed to explain how multilayered connections affect the linear stability of synchronization in dynamical systems. However, the resulting equations are computationally expensive, and therefore difficult, if not impossible, to solve for large systems. To bridge this gap, we develop a mean-field theory of synchronization for networks with multiple interaction layers. By assuming quasi-identical layers, we obtain accurate assessments of synchronization stability that are comparable with the exact results. In fact, the accuracy of our theory remains high even for networks with very dissimilar layers, thus posing a general question about the mean-field nature of synchronization stability in multilayer networks. Moreover, the computational complexity of our approach is only quadratic in the number of nodes, thereby allowing the study of systems whose investigation was thus far precluded.

Original language	English
Article number	121
Number of pages	6
Journal	Communications Physics
Volume	5
Early online date	18 May 2022
DOIs	https://doi.org/10.1038/s42005-022-00897-0
Publication status	E-pub ahead of print - 18 May 2022

Bibliographical note

This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/ licenses/by/4.0/.

Funder

Funding Information: CIDG acknowledges support from UKRI under Future Leaders Fellowship grant number MR/T020652/1. SFL and JGG acknowledge support from MINECO and FEDER funds (Projects No. FIS2017-87519-P, No. FIS2017-90782-REDT (IBERSINC), and No. PID2020-113582GB-I00) and from the Departamento de Industria e Innovación del Gobierno de Aragón y Fondo Social Europeo (FENOL group, grant E36-20r). SFL acknowledges financial support by Gobierno de Aragón through the Grant defined in ORDEN IIU/1408/2018.

Keywords

Applied mathematics
Complex networks
Nonlinear phenomena

Access to Document

10.1038/s42005-022-00897-0Licence: CC BY

PublishedFinal published version, 1 MBLicence: CC BY

Cite this

@article{62b8fdb177824b598e7e7777d89eceb6,

title = "Mean-field nature of synchronization stability in networks with multiple interaction layers",

abstract = "The interactions between the components of many real-world systems are best modelled by networks with multiple layers. Different theories have been proposed to explain how multilayered connections affect the linear stability of synchronization in dynamical systems. However, the resulting equations are computationally expensive, and therefore difficult, if not impossible, to solve for large systems. To bridge this gap, we develop a mean-field theory of synchronization for networks with multiple interaction layers. By assuming quasi-identical layers, we obtain accurate assessments of synchronization stability that are comparable with the exact results. In fact, the accuracy of our theory remains high even for networks with very dissimilar layers, thus posing a general question about the mean-field nature of synchronization stability in multilayer networks. Moreover, the computational complexity of our approach is only quadratic in the number of nodes, thereby allowing the study of systems whose investigation was thus far precluded.",

keywords = "Applied mathematics, Complex networks, Nonlinear phenomena",

author = "{del Genio}, Charo and Sergio Faci-L{\'a}zaro and Jes{\'u}s G{\'o}mez-Garde{\~n}es and Stefano Boccaletti",

note = "This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article{\textquoteright}s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article{\textquoteright}s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/ licenses/by/4.0/.",

year = "2022",

month = may,

day = "18",

doi = "10.1038/s42005-022-00897-0",

language = "English",

volume = "5",

journal = "Communications Physics",

issn = "2399-3650",

publisher = "Nature Research",

}

TY - JOUR

T1 - Mean-field nature of synchronization stability in networks with multiple interaction layers

AU - del Genio, Charo

AU - Faci-Lázaro, Sergio

AU - Gómez-Gardeñes, Jesús

AU - Boccaletti, Stefano

N1 - This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/ licenses/by/4.0/.

PY - 2022/5/18

Y1 - 2022/5/18

N2 - The interactions between the components of many real-world systems are best modelled by networks with multiple layers. Different theories have been proposed to explain how multilayered connections affect the linear stability of synchronization in dynamical systems. However, the resulting equations are computationally expensive, and therefore difficult, if not impossible, to solve for large systems. To bridge this gap, we develop a mean-field theory of synchronization for networks with multiple interaction layers. By assuming quasi-identical layers, we obtain accurate assessments of synchronization stability that are comparable with the exact results. In fact, the accuracy of our theory remains high even for networks with very dissimilar layers, thus posing a general question about the mean-field nature of synchronization stability in multilayer networks. Moreover, the computational complexity of our approach is only quadratic in the number of nodes, thereby allowing the study of systems whose investigation was thus far precluded.

AB - The interactions between the components of many real-world systems are best modelled by networks with multiple layers. Different theories have been proposed to explain how multilayered connections affect the linear stability of synchronization in dynamical systems. However, the resulting equations are computationally expensive, and therefore difficult, if not impossible, to solve for large systems. To bridge this gap, we develop a mean-field theory of synchronization for networks with multiple interaction layers. By assuming quasi-identical layers, we obtain accurate assessments of synchronization stability that are comparable with the exact results. In fact, the accuracy of our theory remains high even for networks with very dissimilar layers, thus posing a general question about the mean-field nature of synchronization stability in multilayer networks. Moreover, the computational complexity of our approach is only quadratic in the number of nodes, thereby allowing the study of systems whose investigation was thus far precluded.

KW - Applied mathematics

KW - Complex networks

KW - Nonlinear phenomena

UR - http://www.scopus.com/inward/record.url?scp=85130260144&partnerID=8YFLogxK

U2 - 10.1038/s42005-022-00897-0

DO - 10.1038/s42005-022-00897-0

M3 - Article

SN - 2399-3650

VL - 5

JO - Communications Physics

JF - Communications Physics

M1 - 121

ER -

Mean-field nature of synchronization stability in networks with multiple interaction layers

Abstract

Bibliographical note

Funder

Keywords

Access to Document

Other files and links

Fingerprint

Cite this