Solution
= 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 $b=0$.
= 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 $b=0$.