# Bifurcation theory

## Study of sudden qualitative behavior changes caused by small parameter changes / From Wikipedia, the free encyclopedia

#### Dear Wikiwand AI, let's keep it short by simply answering these key questions:

Can you list the top facts and stats about Bifurcation theory?

Summarize this article for a 10 year old

**Bifurcation theory** is the mathematical study of changes in the qualitative or topological structure of a given family of curves, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations. Most commonly applied to the mathematical study of dynamical systems, a **bifurcation** occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden 'qualitative' or topological change in its behavior.[1] Bifurcations occur in both continuous systems (described by ordinary, delay or partial differential equations) and discrete systems (described by maps).

The name "bifurcation" was first introduced by Henri Poincaré in 1885 in the first paper in mathematics showing such a behavior.[2]

Oops something went wrong: