Catastrophe
For any system that seeks to minimize a function, only seven different local forms of catastrophe "typically" occur for four or fewer variables:
1. Fold catastrophe,
2. Cusp catastrophe,
5. Elliptic umbilic catastrophe,
6. Hyperbolic umbilic catastrophe, and
7. Parabolic umbilic catastrophe.
More specifically, for any system with fewer than five control factors and fewer than three behavior axes, these are the only seven catastrophes possible. The following tables gives the possible catastrophes as a function of control factors and behavior axes.
The following table gives prototypical examples for equations showing each type of catastrophe.
See also
Butterfly Catastrophe, Catastrophe Theory, Cusp Catastrophe, Elliptic Umbilic Catastrophe, Fold Catastrophe, Hyperbolic Umbilic Catastrophe, Parabolic Umbilic Catastrophe, Swallowtail CatastropheExplore with Wolfram|Alpha
References
Sanns, W. Catastrophe Theory with Mathematica: A Geometric Approach. Germany: DAV, 2000.Referenced on Wolfram|Alpha
CatastropheCite this as:
Weisstein, Eric W. "Catastrophe." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Catastrophe.html