Catastrophe theory  

From The Art and Popular Culture Encyclopedia

Jump to: navigation, search

Related e



Kunstformen der Natur (1904) by Ernst Haeckel
Kunstformen der Natur (1904) by Ernst Haeckel

In mathematics, catastrophe theory is a branch of bifurcation theory in the study of dynamical systems; it is also a particular special case of more general singularity theory in geometry.

Bifurcation theory studies and classifies phenomena characterized by sudden shifts in behavior arising from small changes in circumstances, analysing how the qualitative nature of equation solutions depends on the parameters that appear in the equation. This may lead to sudden and dramatic changes, for example the unpredictable timing and magnitude of a landslide.

Catastrophe theory, which originated with the work of the French mathematician René Thom in the 1960s, and became very popular due to the efforts of Christopher Zeeman in the 1970s, considers the special case where the long-run stable equilibrium can be identified with the minimum of a smooth, well-defined potential function (Lyapunov function).

Small changes in certain parameters of a nonlinear system can cause equilibria to appear or disappear, or to change from attracting to repelling and vice versa, leading to large and sudden changes of the behaviour of the system. However, examined in a larger parameter space, catastrophe theory reveals that such bifurcation points tend to occur as part of well-defined qualitative geometrical structures.

See also

Unless indicated otherwise, the text in this article is either based on Wikipedia article "Catastrophe theory" or another language Wikipedia page thereof used under the terms of the GNU Free Documentation License; or on original research by Jahsonic and friends. See Art and Popular Culture's copyright notice.

Personal tools