Catastrophe theory

Summary

Catastrophe theory is the part of singularity theory that studies how the critical points of a smooth family of functions change as the parameters vary. Small smooth changes of the parameters can make a minimum vanish, so that the state jumps suddenly; such a jump is a catastrophe. René Thom showed that for families with at most four parameters only seven elementary catastrophes occur generically, such as the fold and the cusp. The theory was popularised by Christopher Zeeman as a model of sudden changes in physical and other systems.