Could anyone give me some pointers on how to make a bifurcation diagram of a two parameter ODE of a harvesting model.
It's $$ \dot{x} = ax\left(1 - \frac{x}{b}\right)- \frac{x^2}{1 + x^2}. $$
If I set the two parts equal, $a\left(1 - \frac{x}{b}\right) = \frac{x}{1 + x^2}$ I see that I can get three, two, or one equilibrium points depending on the slope of the line by changing $a$ and $b$ , yet I'm stumped on how to diagram such a thing to find bifurcation points.
I'm not looking for a solution as much as source or tip to get started on two parameter problems.