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. 2022 Oct 6;12:16793. doi: 10.1038/s41598-022-19994-9

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Open AccessThis 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 licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence 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 licence, visit http://creativecommons.org/licenses/by/4.0/.

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Bifurcation sets and numerical simulations for a single Wilson–Cowan node (12), (13) with $c_{1} = c_{2} = c_{3} = 10$ and $c_{4} = - 2$ . LHS: The dashed curve denotes the saddle-node bifurcation set and the solid curve the Hopf bifurcation set. RHS: (a, b) and (c, d) display phase plane and time courses for oscillatory and steady state solutions (for parameter values indicated by the cross and triangle in the left-hand panel) of Eqs. (12), (13) with $ϵ = 0$ .