Past exam of the mathematical and Computational Biology course of the University of Cambridge / 2024 / Paper 1 / B2 / a / Solution

For the squared-denominator population map, a fixed point satisfiesThere is always the extinction fixed point $\bar{x}=0$. For a positive fixed point, divide by $\bar{x}$ and use $b+\bar{x}>0$ to obtainAt equality the candidate merges with zero and is not positive.