catastrophe theory
In mathematics, catastrophe theory seeks to describe the structure of phenomena in which sharply discontinuous results follow from continuous processes. The theory was first developed by French mathematician Rene Thom in a paper published in 1968, but it has its roots in such fields as topology and dynamical system theory.
While its subjects would include actual catastrophes such as a girder suddenly buckling, it is intended to apply to an abrupt change in any process.
When catastrophe theory first appeared, controversy was created by some of the claims being made for its possible applications to real-life situations in such diverse fields as sociology and the behavioral sciences. In the following years, however, the theory has become an established area of mathematical research and has demonstrated its usefulness in the study of many problems in physics; its wider relevance continues to be explored.