Solution (source code)

= Solution

For $b=0,a>0$, the nonzero branches $x=\pm\sqrt{(1-\mu)/a}$ exist for $\mu<1$ and have multiplier $3-2\mu>1$, so both repel. Zero changes from attracting below one to repelling above one: the bifurcation at one is a subcritical <pitchfork bifurcation>. At minus one its multiplier crosses $-1$, producing a supercritical <period-doubling bifurcation>; the newly stable small two-cycle lies on the side $\mu<-1$.