catastrophe theory
a mathematical theory regarding discontinuous (discrete) changes in one variable as a function of continuous change in some other variable or variables. It proposes that a small change in one factor may cause an abrupt and large change in another, for example, the dramatic change in the physical properties of water as the temperature reaches 0 °C or 100 °C (32 °F or 212 °F). Catastrophe theory models are classified according to the number of control parameters, the most common being the cusp catastrophe model, in which two control parameters are varied simultaneously. This model has been used in various areas of investigation, such as figure perception, cognitive development, industrial accidents, and task performance. The cusp catastrophe model of anxiety and task performance, for example, proposes that under conditions of high anxiety, as physiological arousal increases, performance will increase to a certain point but that past this
point a catastrophic drop in performance will occur. To regain an optimal level of performance, a substantial lowering of physiological arousal is necessary. [originated by French mathematician René Frédéric Thom (1923–2002)]