Definition:Catastrophe Theory
Definition
Catastrophe theory is a branch of bifurcation theory in the study of dynamical systems.
It is also a particular special case of more general singularity theory in geometry.
It is based on the modelling of a dynamical system as a set of points in $n$-dimensional space.
It concentrates on topological classification of such sets, connecting sudden discontinuous changes (that is, "catastrophes") with changes in topology.
The theory has been applied to many fields, such as sociology, economics, engineering and linguistics.
Also see
- Results about catastrophe theory can be found here.
Historical Note
Catastrophe theory was developed by René Frédéric Thom in $1972$ to explain aspects of biological growth.
In particular, it seeks to explore the phenomenon in which slow growth is accompanied by "catastrophic" changes in form.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): catastrophe theory
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): catastrophe theory