| Catastrophe Model | Control Parameters | State Variables | Potential function |
| Fold | 1 | 1 |
|
| Cusp | 2 | 1 |
|
| Dovetail | 3 | 1 |
|
| Butterfly | 4 | 1 |
|
| Oval umbilici point | 3 | 2 |
|
| Elliptic umbilici point | 3 | 2 |
|
| Parabolic umbilici point | 4 | 2 |
|