Catastrophe theory

Subject-matter

Modern catastrophe theory is a mathematical theory that deals with discontinuous transitions in dynamic systems. Transitions of this kind (“singularities”) can be grouped in various classes, each distinguished by certain formal characteristics, e.g., fold catastrophes, cusp catastrophes, swallow-tail catastrophes, butterfly catastrophes and so forth. In all, catastrophe theory distinguishes seven basic types of discontinuous change. One of these is of particular interest: branching behaviour (“bifurcation”) of dynamical systems in dependence upon particular adjustable parameters.

Catastrophe theory is applied above all in physics, for example in connection with chaos theory, but also in biology, economics, linguistics and psychology. It was developed by mathematicians René Thom and Wladimir I. Arnold, and it became more widely known especially through the work of Christopher E. Zeemann, who demonstrated the breadth of its possible areas of application.









       


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