I'm given a pair of functions:
$$ \dot u = \frac{\alpha_1}{1 + v^2} - u \\ \dot v = \frac{\alpha_2}{1 + u^2} - v $$
where $\alpha_1$ and $\alpha_2$ are the expression rates of two proteins $u$ and $v$. The behavior of this system is that when one protein is high, the other should be low.
When $\alpha_1 = \alpha_2 = 2$ there are two isolated equilibra corresponding to having one protein be high and the other low.
My question is how could I show that these equilibria are unstable? Not only that but I also need to show that the set of points where $u=v$ consists of all unstable equilibria.