catastrophe theory


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Related to catastrophe theory: Chaos theory

catastrophe theory

n
(Mathematics)
a. a mathematical theory that classifies surfaces according to their form
b. the popular application of this theory to the explanation of abruptly changing phenomena, as by the discontinuity of a line on the topmost fold of a folded surface
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Ten artists will join forces on Friday at the Nicosia Municipal Arts Centre for the opening of their group exhibition entitled The Presence of Absence, or the Catastrophe Theory.
In addition, many experts and scholars have analyzed and summarized the coal and gas outburst mechanism based on the catastrophe theory, which greatly promoted the theoretical research process of coal and gas outburst accidents.
Then catastrophe fuzzy membership function is the combination of catastrophe theory and fuzzy mathematics.
Catastrophe theory was first put forward by the French scholar Rene Thom in 1972, and the application foundation of catastrophe theory, singularity theory and topology, was given in his book "Structural Stability and Morphogenesis"--Based on the mutation type of the critical points of potential functions, it explores the inherent mechanism of the discontinuous sudden change of potential function at different critical points by topological method.
The author has organized the main body of his text in fourteen chapters devoted to cellular automata and spatial diffusion models, artificial neural networks, ant colony optimization, organization and organizational theory, self-organization, intelligence principles, agent-based modeling, catastrophe theory and methods, fish and particle swarm optimization, and many other related subjects.
In fact, in the letter to the mathematician and creator of catastrophe theory Rene Thom that appears as the second paper in the volume, Toussaint himself underlines certain parallelisms between some of the mathematician's proposals and his linguistic model.
As a mathematical model characterized by dialectic and simple construction, catastrophe theory (CT) generally applies to systems that may respond to continuous changes in control variables through a discontinuous change from one equilibrium state to another.
Another avenue would be to explore if Thom's "catastrophe theory" [17] (or other more general theories of bifurcation) applied to particle physics could spontaneously reproduce multiple generations, as it is known to include stable/unstable multiple solutions.
utilized the catastrophe theory to set up vertical deformation model of the overlapping roof in the mined-out areas and put forward the criteria for evaluating the roof stability [6].
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