Steady states in a differential system Given the following model

$$\begin{cases} \frac{du}{d\tau} = \beta u \big(1- \frac{u}{v}\big)\\
\frac{dv}{d\tau} = v(1-v) - \alpha uv
\end{cases}$$

where $\alpha, \beta \geq 0$.

I'm trying to calculate and determine the stability of the steady states. The only one I can find though is $(u,v) = (0,1)$. 

I've tried letting $\dot{u} = \dot{v} = 0$ but it doesn't make things easier.
This differential system is found in population dynamics. 

You will find a general setting in the excellent document "Modeling Population Dynamics" (https://staff.fnwi.uva.nl/a.m.deroos/downloads/pdf_readers/syllabus.pdf): see equations (7.2) page 137.
This differential system is found in population dynamics. 

You will find a general setting in the excellent document "Modeling Population Dynamics" (https://staff.fnwi.uva.nl/a.m.deroos/downloads/pdf_readers/syllabus.pdf): see equations (7.2) page 137.