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. 2018 May 3;8:6949. doi: 10.1038/s41598-018-24670-y

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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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Noise synchronizes interconnected networks of relaxation oscillators. (A) Space-time diagram of $x_{i}^{(α)} (t)$ for 50 of the $N = 200$ networks with N_α = 80 oscillators each. Networks are not synchronized for vanishing noise, σ = 0 (A1). Partial, oscillatory synchronization for σ = 0.025 (A2). Almost complete synchronization for σ = 0.07 (A3). (B) Lower panel: temporal mean and standard deviation of the global order parameter r_global showing a discontinuous transition to an ordered regime as the uncorrelated noise is increased. Upper panel: mean local order parameter ${\bar{r}}_{l o c a l}$ decreases with noise.