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. 2018 Jul 2;8:9910. doi: 10.1038/s41598-018-28236-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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Synchronization transition. The synchronization order parameter R and its variance σ_R are shown for D = 1 (panels (a and d)), D = 2 (panels (b and e)) and D = 3 (panels (c and f)). Different lines are drawn for different networks sizes: N = 100 (blue), 200 (green), 400 (red), 800 (cyan), 1600 (pink) and 3200 (black). The data are averaged over 50 realizations of the CNMs and the internal frequencies. A finite size scaling analysis shows decay in the synchronization order parameter with network size for every dimension (from 2 to 4) indicating that synchronization fades away in the infinite-network-size (thermodinamic) limit⁴³.