To find the equilibrium points solve:
simultaneously. Next need to linearize them and then solve for the eigenvalues of the resulting matrix. The form of the eigenvalues determines the type of equilibrium point. May I suggest "Differential Equations" by Blanchard, Devaney, and Hall". I think it does a nice job of explaining these in great detail at a confortable level. I'll try and work on it today and see what I get.