Symmetries and cluster synchronization in multilayer networks

Fabio Rossa, Louis Pecora, Karen Blaha, Afroza Shirin, Isaac Klickstein and Francesco Sorrentino ()
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Fabio Rossa: University of New Mexico
Louis Pecora: U.S. Naval Research Laboratory
Karen Blaha: University of New Mexico
Afroza Shirin: University of New Mexico
Isaac Klickstein: University of New Mexico
Francesco Sorrentino: University of New Mexico

Nature Communications, 2020, vol. 11, issue 1, 1-17

Abstract: Abstract Real-world systems in epidemiology, social sciences, power transportation, economics and engineering are often described as multilayer networks. Here we first define and compute the symmetries of multilayer networks, and then study the emergence of cluster synchronization in these networks. We distinguish between independent layer symmetries, which occur in one layer and are independent of the other layers, and dependent layer symmetries, which involve nodes in different layers. We study stability of the cluster synchronous solution by decoupling the problem into a number of independent blocks and assessing stability of each block through a Master Stability Function. We see that blocks associated with dependent layer symmetries have a different structure to the other blocks, which affects the stability of clusters associated with these symmetries. Finally, we validate the theory in a fully analog experiment in which seven electronic oscillators of three kinds are connected with two kinds of coupling.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:nat:natcom:v:11:y:2020:i:1:d:10.1038_s41467-020-16343-0

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DOI: 10.1038/s41467-020-16343-0

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