TABLE 2.
Definitions and examples of codimension-one and -two bifurcations
| Codimension-one bifurcations
| ||||
|---|---|---|---|---|
| Full name | Abbreviation | From/to | To/from | 1D example |
| Saddle-node | SN | 3 steady states | 1 steady state |  |
| Supercritical Hopf | HBsup | 1 stable steady state | Unstable steady state + small amplitude, stable limit cycle | |
| Subcritical Hopf | HBsub | 1 unstable steady state | Stable steady state + small amplitude, unstable limit cycle | |
| Cyclic-fold | CF | No oscillatory solutions | 1 stable oscillation + 1 unstable oscillation | |
| Saddle-node infinite-period | SNIPER | 3 steady states | Unstable steady state + large amplitude oscillation | |
| Saddle-loop | SL | Unstable steady state (saddle) | Unstable steady state + large amplitude oscillation | |
| Codimension-two bifurcations
| |||||
|---|---|---|---|---|---|
| Full name | Abbreviation | From/to | To/from | 1D example | 2D example |
| Saddle-node loop | SNL | SN + SL | SNIPER |  |
|
| Degenerate Hopf | dHB | HBsup | HBsub + CF | ||
| Takens-Bogdanov | TB | SN + HB + SL | SN | ||
| CUSP | CUSP | Bistability (2 SN) | Monostability | ||