I'm trying to evaluate this system, by finding and categorizing 4 equilibria points as stable, asymptotically stable, or unstable (nodes, saddles, foci, or centers). Then I have to determine if this describes a species coexistence or competitive exclusion scenario.

I have found three of the 4 equil. points, and evaluated them in a Jacobi matrix. The fourth (positive equil. point) seems to not exist....as I solve the system to find that -0.5=0, which is obviously false.

I'm afraid I may have made a mistake somewhere. Can I get a push in the right direction?