 Solution

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: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 $-N^{\ast }$, 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.