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

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

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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 languageEnglish
Article number121
Number of pages6
JournalCommunications Physics
Early online date18 May 2022
Publication statusE-pub ahead of print - 18 May 2022

Bibliographical note

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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.


  • Applied mathematics
  • Complex networks
  • Nonlinear phenomena


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