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. 2022 Jul 8;84(8):85. doi: 10.1007/s11538-022-01046-y

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© The Author(s) 2022

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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Fig. 3 — Steady state solutions for $Q_{3}^{(0)}$ as a function of the inlet haematocrit, $H_{0}$ , when $α = 0.45 .$ Each solution branch is illustrated with a different line colour, with the black line representing the trivial solution. Solid and dashed lines correspond to stable and unstable solutions, respectively. The region of Hopf instability analysed in Sects. 3.3–3.4 is not indicated in this figure. The grey area bounded by the dash-dotted lines is the region in which the steady-state solutions have no haematocrit in vessel 3. The inset shows an enlarged image of the two bifurcations: (i) the saddle-node bifurcation, $H_{S}$ , from which the red and blue solutions originate; (ii) the transcritical bifurcation, $H_{T}$ , at which the blue and black (trivial) solutions exchange stability (Color figure online)