$\dot{x}=x-rx^{3}=f\left ( r,x \right )$
Attempt to find the control parameter:
$f'\left ( r,x \right )=1-3rx^{2}$
$f'\left ( r,x \right )=0 \Rightarrow 1-3rx^{2}\Rightarrow x=\pm \sqrt{\frac{1}{3r}}$
Now, $f\left ( r,x \right )=0 \Rightarrow 1-rx^{2}=0$
Substituting $x=\pm \sqrt{\frac{1}{3r}}$ into $f\left ( r,x \right )=0 \Rightarrow 1-rx^{2}=0$ doesn't give me anything meaningful due to the fact that the variable r is cancelled.
Is there a trick to this or am I overlooking something?