Solution
= Solution
At a nonzero <fixed point> of the nonlinear <stage-structured population model>, the adult balance gives $d\bar z=c\bar y$. Substitute $\bar y=d\bar z/c$ into the juvenile equation and cancel $\bar z>0$:
$$
\frac dc=\frac r{(b+\bar z)^2}.
$$
Thus
$$
\boxed{\bar z=\sqrt{\frac{cr}{d}}-b,\qquad
\bar y=\frac dc\left(\sqrt{\frac{cr}{d}}-b\right)}.
$$
Both coordinates are positive precisely when \b[$\boxed{cr>db^2}$.]