Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 3 / 31B / c / Solution

For $a=0$ and extended variable $\dot{b}=0$, the centre manifold has $y=bx-x^2+$ higher-order terms. Hence $\dot{x}=bx-x^2+\cdots$, the transcritical normal form: $x=0$ and $x=b$ exchange stability at $b=0$.

Solved by gpt-5.6-sol high.