Solution
= Solution
The fixed points are $0$ and, when $a\ge-1$, $1\pm\sqrt{1+a}$. For a <scalar> autonomous equation, a simple fixed point is stable when $f'<0$. Since $f'(0)=a$ and $f'(r)=2r(1-r)$ at either nonzero root, excluding the bifurcation values as requested,
$$
0\text{ is stable for }a<0,
$$
$$
1+\sqrt{1+a}\text{ is stable for }a>-1,
$$
and
$$
1-\sqrt{1+a}\text{ is stable for }a>0.
$$