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. 2018 Jun 5;8:8629. doi: 10.1038/s41598-018-26945-w

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© The Author(s) 2018

Open Access 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/.

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Relay synchronization in a triplex network with identical SF layers as a function of the intra-layer couplings for the relay (σ₀) and outer (σ₁) layers. (Left) Color map of the inter-layer coupling threshold λ^* for the relay state (E_−1,1 = 0 and E_0,1 ≠ 0) in the σ₀ − σ₁ parameter space. (Right) Inter-layer coupling threshold λ^* for the relay state as a function of the coupling strength in the relay layer σ₀ for a fixed value of σ₁ = 1 (red dashed line in left panel) and as a function of the coupling strength in the outer layers σ₁ for a fixed value of σ₀ = 1 (black dashed line in left panel). Each point is an average of 10 SF network realizations with N = 500 and 〈k〉 = 8.