I have the following equation $\dot{x}=-x^3+bx$. I know the equation has three equilibrium points for $b>0$: $0$ (unstable) and $\pm\sqrt b$ (stable). .
My question is can I make the strength of the attractor at one of the stable points (let's choose $\sqrt b$) while maintaining the same attractor strength at the other stable point ($-\sqrt b$)?
If I were to multiply the RHS by a constant $\alpha>1$ such that $\dot{x}=\alpha(-x^3+bx)$, I could increase the slope at each fixed point. However, I cannot determine how to increase the slope only at a single fixed point, if it is possible.
Any help is greatly appreciated.