For each of the one-dimensional systems

(i) $\dot{x}=\mu^{2}-a^{2}+2 a x^{2}-x^{4}$,

(ii) $\dot{x}=x\left(\mu^{2}-a^{2}+2 a x^{2}-x^{4}\right)$,

determine the location and stability of all the fixed points. For each system sketch bifurcation diagrams in the $(\mu, x)$ plane in each of the two cases $a>0$ and $a<0$. Identify and carefully describe all the bifurcation points that occur.

[Detailed calculations are not required, but bifurcation diagrams must be clearly labelled, and the locations of bifurcation points should be given.]