---
tag: N087STXZKG
kind: concept
name: Crisis
msc: [37G35, 37D45]
sources:
  - url: https://en.wikipedia.org/wiki/Crisis_(dynamical_systems)
same_as:
  wikidata: Q5185947
  wikipedia: Crisis (dynamical systems)
---

## Summary

A crisis is a bifurcation in which a chaotic [[attractor|7FWX24X5MW]] suddenly changes size or disappears as a parameter varies.
It happens when the attractor collides with an unstable periodic orbit or with its stable manifold.
In a boundary crisis the attractor touches the boundary of its basin and is destroyed; in an interior crisis it suddenly grows.
The notion was introduced by Grebogi, Ott and Yorke.

## Explanations

### L1 human

A chaotic system can wander inside a bounded region for ever, but the region itself depends on the parameters.
At a crisis the region abruptly bumps into an unstable orbit, a kind of trapdoor.
If the trapdoor leads out of the basin, orbits that used to stay chaotic forever now escape after a long chaotic transient.
If it leads to another part of space, the chaotic region suddenly becomes much larger.