Abstract: Publisher SummaryThis chapter discusses the origin of catastrophe theory. Catastrophe theory deals with the nonlinear phenomena in which a continuous change in control parameters results in a discontinuous alteration of a quantity characterizing the examined system. It is well suited for the investigation of the nonlinear equations of chemical kinetics, describing chemical reactions. Chemical reactions without diffusion are classified from the standpoint of catastrophe theory, and the theoretical results for the reactions with diffusion are presented. The connections among the various domains of physics and chemistry dealing with nonlinear phenomena and the progress achieved in catastrophe theory are discussed. The theory describes only such phenomena whose form is resistant to perturbations–– that is, structurally stable. Catastrophe theory describes changes in the form taking place as a result of continuous variations of control parameters, emphasizing qualitative, structurally stable changes in the form. The most important notions of elementary catastrophe theory, such as structural stability, sensitive state, codimension, universal unfolding, have formed the basis for generalizations going beyond gradient systems.
Publication Year: 1992
Publication Date: 1992-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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