Equilibrium point | Scenario 1 | Scenario 2 | Scenario 3 | Scenario 4 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(det J\) | \(tr J\) | Result | \(det J\) | \(tr J\) | Result | \(det J\) | \(tr J\) | Result | \(det J\) | \(tr J\) | Result | |
\(O\left(0, 0\right)\) | \(+\) | \(-\) | ESS | \(-\) | \(\pm\) | Saddle | \(-\) | \(\pm\) | Saddle | \(+\) | \(+\) | Unstable |
\(A\left(0, 1\right)\) | \(+\) | \(+\) | Unstable | \(-\) | \(\pm\) | Saddle | \(+\) | \(+\) | Unstable | \(-\) | \(\pm\) | Saddle |
\(B\left(1, 0\right)\) | \(+\) | \(+\) | Unstable | \(+\) | \(+\) | Unstable | \(-\) | \(\pm\) | Saddle | \(-\) | \(\pm\) | Saddle |
\(C \left(1, 1\right)\) | \(+\) | \(-\) | ESS | \(+\) | \(-\) | ESS | \(+\) | \(-\) | ESS | \(+\) | \(-\) | ESS |
\(E\left({x}^{*}, {y}^{*}\right)\) | \(-\) | 0 | Saddle | Â | Â | None | Â | Â | None | Â | Â | None |