Ricker model

$\displaystyle \frac{dN}{dt}=\frac{rN}{e^{\beta N}}$

Beverton-Holt model

$\displaystyle \frac{dN}{dt}=\frac{rN}{\alpha +N}$

To get steady states, do I just set $\displaystyle \frac{dN}{dt}=0$ for both models?

I'm not sure how to get stability. Do I just take the derivative of both models and plug in the steady states?