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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References

Altmann, G. & W. A. Koch
(eds.) 1988Systems. New Paradigms for the Human Sciences. de Gruyter. Google Scholar
Brandt, P. A.
1992La charpente modale du sens. Aarhus University Press & John Benjamins. DOI logoGoogle Scholar
Gilmore, R.
1982Catastrophe theory for scientists and engineers. Wiley. Google Scholar
Haken, H.
1977Synergetics. Springer. DOI logoGoogle Scholar
Haken, H. & M. Stadler
(eds.) 1990Synergetics of cognition. Springer. DOI logoGoogle Scholar
Herzel, H. & K. Wermke
1989Bifurcation and chaos in newborn infant cries. Ms. Google Scholar
Majthay, A.
1985Foundations of catastrophe theory. Pitman. Google Scholar
Petitot, J.
1985Morphogenèse du sens. Presses University de France. Google Scholar
1992Physique du sens. Editions du CNRS. Google Scholar
Saunders, P. T.
1980An introduction to catastrophe theory. Cambridge University Press. DOI logoGoogle Scholar
Thom, R.
1977Stabilité structurelle et morphogénèse. Interéditions. Google Scholar
1988Esquisse d'une sémiophysique. Interéditions. Google Scholar
1989René Thom expliqué par lui-même. Guenot. Google Scholar
Wildgen, W.
1982Catastrophe theoretic semantics. John Benjamins. DOI logoGoogle Scholar
1983Dialogdynamik. Papiere zur Linguistik 29: 3–21. Google Scholar
1985Archetypensemantik. Narr. Google Scholar
1986Synergetische Modelle in der Soziolinguistik. Zeitschrift für Sprachwissenschaft 5: 105–137. DOI logoGoogle Scholar
1990Basic principles of self-organization in language. In H. Haken & M. Stadler (eds.): 415–426. DOI logoGoogle Scholar
1994Process, image, and meaning. John Benjamins. DOI logoGoogle Scholar
1998Chaos, Fractals and Dissipative Structures in Language. Or the End of Linguistic Structuralism. In: G. Altmann & W. A. Koch (eds.): 596–620. DOI logoGoogle Scholar
2004The Evolution of Human Language. Scenarios, Principles, and Cultural Dynamics. John Benjamins. DOI logoGoogle Scholar
forthcomingThom's Theory of «saillance» and «prégnance» and Modern Evolutionary Linguistics. In P. A. Brandt & W. Wildgen (eds.) Semiosis and Catastrophes. René Thom's Semiotic Heritage.Lang. Google Scholar
Wildgen, W. & P. Plath
2005Katastrophen- und Chaostheorie in der linguistischen Modellbildung. In R. Köhler, G. Altmann & G. Pietrow (eds.) Quantitative Linguistics/Quantitative Linguistik. Ein Internationales Handbuch: 688–705. de Gruyter. Google Scholar
Woodcock, A. & M. Davis
1978Catastrophe theory. Dutton. Google Scholar
Zeeman, C.
1977Catastrophe theory. Addison-Wesley. Google Scholar