Past exam of the mathematical and Computational Biology course of the University of Cambridge / 2024 / Paper 1 / B2 / e / 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 $\bar{z}>0$:ThusBoth coordinates are positive precisely when $\boxed{cr>d{b}^2}$.