Catastrophe theory studies how the qualitative nature of equation solutions depends on the parameters that appear in the equations. Subspecializations include bifurcation theory, nonequilibrium thermodynamics, singularity theory, synergetics, and topological dynamics. For any system that seeks to minimize a function, only seven different local forms of catastrophe "typically" occur for four or fewer variables.
Catastrophe Theory
See also
CatastropheExplore with Wolfram|Alpha
References
Arnold, V. I. Catastrophe Theory, 3rd ed. Berlin: Springer-Verlag, 1992.Dujardin, L. "Catastrophe Teacher: An Introduction for Experimentalists." http://perso.wanadoo.fr/l.d.v.dujardin/ct/eng_index.html.Gilmore, R. Catastrophe Theory for Scientists and Engineers. New York: Dover, 1993.Guckenheimer, J. "The Catastrophe Controversy." Math. Intelligencer 1, 15-20, 1978.Sanns, W. Catastrophe Theory with Mathematica: A Geometric Approach. Germany: DAV, 2000.Saunders, P. T. An Introduction to Catastrophe Theory. Cambridge, England: Cambridge University Press, 1980.Stewart, I. The Problems of Mathematics, 2nd ed. Oxford, England: Oxford University Press, p. 211, 1987.Thom, R. Structural Stability and Morphogenesis: An Outline of a General Theory of Models. Reading, MA: Addison-Wesley, 1993.Thom, R, "Autobiography of René Thom." In Fields Medallists Lectures (Ed. M. Atiyah and D. Iagolnitzer). Singapore, pp. 71-76, 1977.Thompson, J. M. T. Instabilities and Catastrophes in Science and Engineering. New York: Wiley, 1982.Weisstein, E. W. "Books about Catastrophe Theory." http://www.ericweisstein.com/encyclopedias/books/CatastropheTheory.html.Woodcock, A. E. R. and Davis, M. Catastrophe Theory. New York: E. P. Dutton, 1978.Zahler, R. and Sussman, H. J. "Claims and Accomplishments of Applied Catastrophe Theory." Nature 269, 759-763, 1977.Zeeman, E. C. Catastrophe Theory--Selected Papers 1972-1977. Reading, MA: Addison-Wesley, 1977.Referenced on Wolfram|Alpha
Catastrophe TheoryCite this as:
Weisstein, Eric W. "Catastrophe Theory." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CatastropheTheory.html