---
tag: 6FKJ6SXP3G
kind: concept
name: Catastrophe theory
msc: [58K35, 37G10]
specializes: [42V5XGZS4F]
sources:
  - url: https://en.wikipedia.org/wiki/Catastrophe_theory
same_as:
  wikidata: Q1345659
  wikipedia: Catastrophe theory
---

## Summary

Catastrophe theory is the part of [[singularity theory|42V5XGZS4F]] that studies how the [[critical points|0YTCMFB4HC]] 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.

## Explanations

### L1 human

Think of a ball resting in a valley of a landscape that slowly changes shape.
Most of the time the ball moves smoothly as the valley shifts.
But if the valley flattens out and disappears, the ball suddenly rolls to another valley far away.
Catastrophe theory describes the few typical ways this can happen.
In the cusp catastrophe, for example, two valleys exist for some settings and the jump between them depends on the direction from which you approach.