Table 3 The Determinant and Trace at each equilibrium point
Equilibrium point | Determinant | Trace |
|---|---|---|
\(O\left(0, 0\right)\) | \(\left({U}_{2}+{S}_{2}-{P}_{2}\right)\left({R}_{2}+{S}_{1}^{^{\prime}}-{C}_{2}\right)\) | \({U}_{2}+{S}_{2}-{P}_{2}+{R}_{2}+{S}_{1}^{^{\prime}}-{C}_{2}\) |
\(A\left(0, 1\right)\) | \(\left({U}_{1}+{S}_{1}-{P}_{1}\right)\left({C}_{2}-{R}_{2}-{S}_{1}^{^{\prime}}\right)\) | \({U}_{1}+{S}_{1}-{P}_{1}+{C}_{2}-{R}_{2}-{S}_{1}^{^{\prime}}\) |
\(B\left(1, 0\right)\) | \(\left({P}_{2}-{U}_{2}-{S}_{2}\right)\left({R}_{1}+{P}_{1}-{C}_{1}\right)\) | \({P}_{2}-{U}_{2}-{S}_{2}+{R}_{1}+{P}_{1}-{C}_{1}\) |
\(C \left(1, 1\right)\) | \(\left({U}_{1}+{S}_{1}-{P}_{1}\right)\left({R}_{1}+{P}_{1}-{C}_{1}\right)\) | \({C}_{1}-{R}_{1}-{U}_{1}-{S}_{1}\) |
\(E\left({x}^{*}, {y}^{*}\right)\)Â Â | \(-\frac{\left({P}_{2}-{U}_{2}-{S}_{2}\right)\left({C}_{2}-{R}_{2}-{S}_{1}^{^{\prime}}\right)\left({U}_{1}+{S}_{1}-{P}_{1}\right)\left({R}_{1}+{P}_{1}-{C}_{1}\right)}{\left({{U}_{1}-{U}_{2}+P}_{2}-{P}_{1}+{S}_{1}-{S}_{2}\right)\left({R}_{1}-{R}_{2}+{P}_{1}-{S}_{1}^{^{\prime}}+{C}_{2}-{C}_{1}\right)}\) | 0 |