= Solution
{c}
The nonnegative <bifurcation diagram> has the branch $N=0$ for every $r>0$, stable for $r<\delta$ and unstable for $r>\delta$. At $r=\delta$ the stable positive branch emerges:
$$
\boxed{N^*(r)=\sqrt{\frac{r-\delta}{b\delta}},\qquad r>\delta.}
$$
The figure in (iv) uses solid curves for stable <steady states> and a dashed curve for the unstable zero branch. At the meeting point the zero <steady state> is nonhyperbolic and attracts from the nonnegative side. If the equation is formally extended to negative $N$, there is also the symmetric branch $-N^*$, giving a <supercritical pitchfork bifurcation>; its negative half is omitted in the biological diagram. This qualification avoids calling the single nonnegative square-root branch a full pitchfork by itself.
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