catastrophe theory


catastrophe theory
a theory, based on topology, for studying discontinuous processes and the mathematical models that describe them.
[1970-75]

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Branch of mathematics (considered a branch of geometry) that explores how gradual changes to a system produce sudden, drastic results (though usually not as dire as the name suggests).

A simple example is how a plastic coffee stirrer subjected to gradually increasing pressure from both ends will suddenly buckle in one direction or another. Other "catastrophes" include optical phenomena such as reflection or refraction of light through moving water. More speculatively, ideas from catastrophe theory have been applied by social scientists to such situations as the sudden eruption of mob violence.

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      in mathematics, a set of methods used to study and classify the ways in which a system can undergo sudden large changes in behaviour as one or more of the variables that control it are changed continuously. Catastrophe theory is generally considered a branch of geometry because the variables and resultant behaviours are usefully depicted as curves or surfaces, and the formal development of the theory is credited chiefly to the French topologist René Thom (Thom, René Frédéric).

      A simple example of the behaviour studied by catastrophe theory is the change in shape of an arched (arch) bridge as the load on it is gradually increased. The bridge deforms in a relatively uniform manner until the load reaches a critical value, at which point the shape of the bridge changes suddenly—it collapses. While the term catastrophe suggests just such a dramatic event, many of the discontinuous changes of state so labeled are not. The reflection or refraction of light by or through moving water is fruitfully studied by the methods of catastrophe theory, as are numerous other optical phenomena. More speculatively, the ideas of catastrophe theory have been applied by social scientists to a variety of situations, such as the sudden eruption of mob violence.

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Universalium. 2010.

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