Fig. 8.

Effect of smoothing the Pries et al. (1989) haematocrit splitting function on the bifurcation to oscillatory solutions. The solid lines correspond to iso-growth-rate contours (the value of $\sigma$ is indicated) for the oscillatory solutions when the smooth splitting function Eq. (56) is used, while the dashed curves were produced using the original, nonsmooth splitting function [Eq. (14), as in Fig. 6]. The iso-growth-rate contours correspond to flow from the bottom to the top branch for $\alpha <1$ and vice versa for $\alpha >1$. The skimming threshold is plotted for reference (thick dashed black line). The inset presents the function $S(\psi )$ [see definition in Eq. (59)] at the location marked by the black rectangle, $(\alpha ,H_0)=(0.58,0.391)$, for the original, nonsmooth (dashed line) and smoothed (solid line) splitting functions. The corresponding steady-state fluxes $Q_3^{(0)}$ obtained using the nonsmooth (smooth) models at that parameter combination are indicated with open (full) blue circles (Color figure online)