Consider a system of the form $$\frac{d}{dt}x \enspace = \enspace 2-\left(b+1\right)x + ax^2y$$ $$\frac{d}{dt}y\enspace=\enspace bx-ax^2y$$
This is the context of some homework I have. I've already proven that one fixed point exists (namely $\left(x^*,y^*\right)=\left(2,\frac{b}{2a}\right)$).
The remainder of the question assumes $a=b=1$. I'm asked to sketch the nullclines and construct a trapping region for the flow. I'm basing my method off of how Strogatz approaches the Selkov model of glycolysis in his textbook. A phase portrait of that model can be found on the 7th slide here.
Constructing the trapping region for my system is almost the same process as how Strogatz does it for glycolysis, but in my case the nullcline associated with $\dot{y}=0$ is asymptotic with the y-axis, whereas Strogatz has a handy y-intercept to work with.
The trapping region should look something like the thing on page 3 here. The difference is that I'm not sure where the upper end of the diagonal line stops and the horizontal line starts.
Thanks.