Table 5 Stability of equilibrium points.
Equilibrium point | Conditions | det(J) symbol | tr(J) symbol | Outcome |
|---|---|---|---|---|
A (0, 1) | \(\:\text{N}\text{e}\text{v}\text{e}\text{r}\:\text{m}\text{e}\text{t}\:\text{s}\text{i}\text{m}\text{u}\text{l}\text{t}\text{a}\text{n}\text{e}\text{o}\text{u}\text{s}\text{l}\text{y}:\:det\left(J\right)>0,\:tr\left(J\right)<0\) | ? | ? | Unstable |
B (0, 0) | \(\:{L}_{1}-{C}_{1}+{R}_{1}-{R}_{2}+{R}_{3}<0\)、\(\:{C}_{3}-\:{C}_{2}+{C}_{4}+{R}_{5}-{R}_{6}<0\) | + | - | ESS |
C (1, 0) | \(\:{L}_{1}-{C}_{1}+{R}_{1}-{R}_{2}+{R}_{3}>0\)、\(\:{C}_{2}-\:{C}_{3}-{C}_{4}+{L}_{2}-{R}_{4}+{R}_{6}>0\) | + | - | ESS |
D (1, 1) | \(\:\text{N}\text{e}\text{v}\text{e}\text{r}\:\text{m}\text{e}\text{t}\:\text{s}\text{i}\text{m}\text{u}\text{l}\text{t}\text{a}\text{n}\text{e}\text{o}\text{u}\text{s}\text{l}\text{y}:\:det\left(J\right)>0,\:tr\left(J\right)<0\) | ? | ? | Unstable |
E (x*, y*) | Always a saddle point | ? | 0 | Saddle point |
