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. 2017 Aug 7;7:7430. doi: 10.1038/s41598-017-07754-z

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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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A cusp bifurcation in a single node with feedback weight, W _F, external input, u, and neurosynaptic state, s. (a) Theoretical model surface (gray) and bifurcation curves (green) plotted in 3D. Parameters of the model are fit to data. (b) Experimental data for increasing (blue surface) and decreasing (red surface) input. Theoretical bifurcation curves – with parameters identical to those in (a) – are projected onto 2D axes. The data surfaces are sliced at the planes: u = 0, s = 0, and W _F = 0.08, and similarly projected onto the axes (red and blue points) to illustrate the reproduction of pitchfork, cusp, and saddle-node bifurcations, respectively.