Editing Catastrophe theory (section)

{{short description|Area of mathematics}}
{{Redirect|Catastrophic event||Catastrophe (disambiguation){{!}}Catastrophe}}
In [[mathematics]], '''catastrophe theory''' is a branch of [[bifurcation theory]] in the study of [[dynamical system]]s; 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 data|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 (mathematics)|magnitude]] of a [[landslide]].

Catastrophe theory 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. It considers the special case where the long-run stable equilibrium can be identified as the minimum of a smooth, well-defined [[scalar potential|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.

In the late 1970s, applications of catastrophe theory to areas outside its scope began to be criticized, especially in biology and social sciences.<ref>{{cite encyclopedia |last1=Murray |first1=Stacey R. |title=The Rise and Fall of Catastrophe Theory |encyclopedia=[[Encyclopedia.com]] |url=https://www.encyclopedia.com/science/encyclopedias-almanacs-transcripts-and-maps/rise-and-fall-catastrophe-theory |access-date=2 November 2021}}</ref><ref>{{cite book |last1=Horgan |first1=John |title=The End of Science: Facing the Limits of Knowledge in the Twilight of the Scientific Age |date=2015 |publisher=Basic Books |location=New York |isbn=978-0-465-05085-7 |page=213}}</ref> Zahler and Sussmann, in a 1977 article in ''[[Nature (journal)|Nature]]'', referred to such applications as being "characterised by incorrect reasoning, far-fetched assumptions, erroneous consequences, and exaggerated claims".<ref>{{cite journal |doi=10.1038/269759a0 |issn=1476-4687 |volume=269 |issue=5631 |pages=759–763 |last1=Zahler |first1=Raphael S. |last2=Sussmann |first2=Hector J. |title=Claims and accomplishments of applied catastrophe theory |journal=Nature |accessdate=2021-11-02 |date=1977 |bibcode=1977Natur.269..759Z |s2cid=4205198 |url=https://www.nature.com/articles/269759a0|url-access=subscription }}</ref> As a result, catastrophe theory has become less popular in applications.<ref>{{cite journal |last1=Rosser |first1=J. Barkley |title=The rise and fall of catastrophe theory applications in economics: Was the baby thrown out with the bathwater? |journal=Journal of Economic Dynamics and Control |date=October 2007 |volume=31 |issue=10 |pages=3255–3280 |doi=10.1016/j.jedc.2006.09.013}}</ref>