Table 4 Expressions for the determinant and trace at each equilibrium point.
Equilibrium point | \(\:det(J\)) | \(\:tr\left(J\right)\) |
|---|---|---|
A (0, 1) | \(\:-({L}_{1}+{R}_{1}-{R}_{2}+{R}_{3})*({C}_{3}-{C}_{2}+{C}_{4}+{R}_{5}-{R}_{6})\) | \(\:{C}_{2}-{C}_{3}-{C}_{4}+{L}_{1}\:{+R}_{1}\:{-R}_{2}{+R}_{3}-{R}_{5}+{R}_{6}\) |
B (0, 0) | \(\:({L}_{1}-{C}_{1}+{R}_{1}-{R}_{2}+{R}_{3})*({C}_{3}-\:{C}_{2}+{C}_{4}+{R}_{5}-{R}_{6})\) | \(\:{C}_{3}-{C}_{2}-{C}_{1}+{C}_{4}+{L}_{1}+{R}_{1}-{R}_{2}+{R}_{3}+{R}_{5}-{R}_{6}\) |
C (1, 0) | \(\:({L}_{1}-{C}_{1}+{R}_{1}-{R}_{2}+{R}_{3})*({C}_{2}-{C}_{3}-{C}_{4}+{L}_{2}-{R}_{4}+\:{R}_{6})\) | \(\:{{C}_{1}-C}_{2}+{C}_{3}+{C}_{4}-{L}_{1}-\:{L}_{2}-{R}_{1}+{R}_{2}-{R}_{3}+{R}_{4}-{R}_{6}\) |
D (1, 1) | \(\:-({L}_{1}+{R}_{1}-{R}_{2}+{R}_{3})*({C}_{2}-{C}_{3}-{C}_{4}+{L}_{2}-{R}_{4}\:{+R}_{6})\) | \(\:{C}_{2}-{C}_{3}-{C}_{4}-{L}_{1}+{L}_{2}-\:{R}_{1}+{R}_{2}-{R}_{3}-{R}_{4}+{R}_{6}\) |
E (\(\:{x}^{\text{*}},\:\:{y}^{\text{*}}\)) | \(\:-\left(\right({L}_{1}+{R}_{1}-{R}_{2}+{R}_{3}\left)*\right({C}_{3\:}-{C}_{2}+{C}_{4}{+R}_{5}{-R}_{6}\left)*\right({L}_{1}-{C}_{1}+{R}_{1}-{R}_{2}+{R}_{3}\left)*\right({C}_{2}-{C}_{3}-{C}_{4}+{L}_{2}-{R}_{4}+{R}_{6}\left)\right)/\left({C}_{1}*\right({L}_{2}-{R}_{4}+{R}_{5}\left)\right)\) | 0 |
