Originated by the French mathematician Rene Thom in the 1960s, catastrophe theory is a special branch of dynamical systems theory . It studies and classifies phenomena characterized by sudden shifts in behavior arising from small changes in circumstances.

Catastrophes are bifurcations between different equilibria, or fixed point attractors. Due to their restricted nature, catastrophes can be classified based on how many control parameters are being simulataneously varied. For example, if there are two controls, then one finds the most common type, called a "cusp" catastrophe. If, however, there are move than five controls, there is no classification.

Catastrophe theory has been applied to a number of different phenomena, such as the stability of ships at sea and their capsizing , bridge collapse, and, with some less convincing success, the fight-or-flight behavior of animals and prison riots.