TABLE 5.
Stability of stationary points and its relation to the eigenvectors of the linearization matrix JM (Eq. A11)
| Character | r1 | r2 | r3 | r4 |
|---|---|---|---|---|
| Stable | Re < 0 | Re < 0 | Re < 0 | Re < 0 |
| Im = 0 | Im = 0 | |||
| Saddle point | Re > 0 | Re < 0 | Re < 0 | Re < 0 |
| Im = 0 | Im = 0 | Im = 0 | Im = 0 | |
| Node | Re < 0 | Re < 0 | Re < 0 | Re < 0 |
| Im = 0 | Im = 0 | Im = 0 | Im = 0 | |
| Hopf-bifurcation | Re = 0 | Re = 0 | Re < 0 | Re < 0 |
| Im = +t | Im = +t | Im = 0 | Im = 0 | |
| Unstable | Re > 0 | Re > 0 | Re > 0 | Re > 0 |
| Im = 0 | Im = 0 |
A saddle node bifurcation occurs when a saddle point and a node merge.