Catastrophe theory

Wolfgang Wildgen
Table of contents

A catastrophe is a type of instability in a simple dynamic system the unfolding of which is structurally stable. Examples of commonly experienced catastrophes are sudden changes in a real system, e.g., the breakdown of stability as in a bridge which collapses. Elementary catastrophe theory considers gradient systems, i.e., systems governed by attractors which are isolated points, every trajectory in these systems going almost instantaneously to stable states. It applies the classification theorem of Thom and Mather, providing a set of seven elementary catastrophes (and their duals): the fold, the cusp, the swallow tail, the butterfly, the hyperbolic, elliptic and parabolic umbilics (cf. Wildgen 1982: 7–9 and 35–94).

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