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. 2017 Aug 10;7:7795. doi: 10.1038/s41598-017-08245-x

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© The Author(s) 2017

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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Ordinal transition networks on the path to phase synchronization of Eq. (8), for three typical coupling strength. (a) Random transitions in the non-sync regime of κ = 0.02 < κ _c1, (b) dominant structure appears in the regime that oscillators k = 1 and k = 2 are phase synchronized, but not with k = 3, κ = 0.06 ∈ [κ _c1, κ _c2], (c) only one transition route of ordinal patterns is observed when all three oscillators are phase locked κ = 0.08 > κ _c2. Thickness of links are determined by the associated frequencies in the transition networks and self-loops are removed. In (a,b), link arrows are suppressed for the ease of visualization.