= Solution
Let $r=Ra-Ra_c$. The <amplitude equation> is $\dot A=A(r-A^2)$. For $r<0$, $A=0$ is the sole equilibrium and every solution tends monotonically to it. At $r=0$, the origin remains attracting but only algebraically. For $r>0$, the origin is unstable and the two equilibria
$$
A_\pm=\pm\sqrt r
$$
are stable: positive initial data tend to $A_+$, negative initial data tend to $A_-$, and $A(0)=0$ remains zero. A plot of $A(t)$ therefore shows a <pitchfork bifurcation normal form> at $Ra=Ra_c$.
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