Talk:Catastrophe theory

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Mathematics needs to be clearer

Needs more clear mathematical explanations; and a separate section on philosophical implications. Right now the philosophy is mixed up with the mathematics, making it quite confusing, and less useful to mathematicians. +sj + 02:18, 25 November 2005 (UTC)[reply]

As far as I know, V = x³ + ax has two unstable fix points and one stable fix point at negative a, which gives a subcritical bifurcation. V = ax - x³ would have been more illustrative because it has two stable fix points and one unstable fix point at positive a which provides pitchfork bifurkation as a prerequisite for cusp catastrophe: V = b + ax - x³. —Preceding unsigned comment added by Regow (talk • contribs) 15:09, 20 November 2010 (UTC)[reply]

Disambiguate catastrophe modeling

Do you think there should be a note near the top or bottom that links to catastrophe modeling, which is the computer modeling of the effects of catastrophic events such as earthquakes and hurricanes, and is not directly related to the catastrophe theory of mathematics?

Done -- Jheald 22:37, 6 December 2005 (UTC)[reply]

Another good addition would be a definition of a mathematical catastrophe at the top of the article. Wiktionary defines "catastrophe (mathematics)" as "a type of bifurcation, where a system shifts between two stable states." This change would prevent anyone from being confused by the figure of a fold catastrophe, which the caption describes as a bifurcation. Robert O'Rourke (talk) 02:52, 26 March 2011 (UTC)[reply]

Interestingly, there is some mathematical connection with catastrophy modelling. In the terms that the catastrophic events happen when a situation moves away from a stable state. Consider a weather system, it normally is in a stable state (say with wind speeds in a certain range) and slight pertubations do not drastically alter the behaviour. For a hurricain to happen the state would need to pass through a mathematical catastrophy to reach a very diferent state charterised by a hurricain. Probably an example of a cusp catastrophy where the state changes from the upper sheat to the lower sheat. --Pfafrich 00:25, 7 December 2005 (UTC)[reply]

The transition that you are talking about is a Hopf bifurcation, in this case from laminar flow to circular flow in a simple model of the flow of a compressible fluid. It can be revealed as an example of a cusp catastrophe if you look at 2-dimensional fluid flow, and convert to polar coordinates. See, for example, Catastrophe Theory for Scientists and Engineers, by Robert Gilmore, pp. 524-529.

Nevertheless, I think it is quite proper to separate catastrophe modeling as it is understood in the insurance business from the mathematical treatment of nonlinear dynamical systems —Aetheling 19:01, 7 August 2006 (UTC)[reply]

Completely inaccesible to laypeople

As a non-mathematician, I was able to understand virtually nothing in this article. A simple google search reveals numerous webpages that are able to conceptually explain what the theory means and why it exists. While this is a common problem in almost all mathematics articles, catastrophe theory is also discussed in non-mathematics circles and needs to be generally accesible in addition to providing more specific information. DJLayton4 (talk) 23:54, 24 November 2008 (UTC)[reply]

I don't think you need to be a full-fledged mathematician to understand this article, but you should have studied mathematics as far as calculus and physics as far as potential energy. It is unreasonable to expect that you should be able to understand an advanced mathematical topic without having studied any mathematics. Robert O'Rourke (talk) 00:39, 26 March 2011 (UTC)[reply]

I reject the obfuscation by Robert O'Rourke, above. Its claim that readers need technical qualifications to understand the theory is wrong, and conflicts with the purpose of an encyclopaedia, which is not written for experts, but for the general, interested reader.

A famous person, whose name escapes me now, said that if you truly understand something properly, you can explain it clearly to an intelligent audience. I have often seen it done, beginning at school.

Einstein wrote a book for laypeople explaining the special and general theories of relativity. The book was in plain English and did not resort to mathematics.

Brian Greene wrote a book a few years ago explaining string theory for the lay reader. The theory is highly abstract and mathematical in origin, yet it was explained in language the non-physicist and non-mathematician could grasp.

Television documentaries have often been used to explain difficult material in common terms, to convey a sense of what is going on.

Years ago, I read an explanation of catastrophe theory for the layperson; I also saw a clearminded documentary about it. I was able to follow these explanations well enough, without any mathematics involved. Regrettably, in the intervening years, my grasp of the theory has grown hazy, but it was clear at the time.

What this article needs, simply, is someone who understands catastrophe theory and at the same time has the ability to convey abstractions in clear, strong, analogical, and metaphorical ways that any intelligent person can understand. It is an error to claim that a reader should have mathematical or physical qualifications to a certain level to grasp catastrophe theory in a useful and meaningful way. It is Wikipedia's purpose to explain to and inform the general reader. If the Encyclopaedia Britannica can provide an approachable explanation of the theory, Wikipedia can and must do the same. — O'Dea (talk) 11:47, 30 September 2018 (UTC)[reply]

Needs some qualification

Neither this article nor this one distinguish chaos from catastrophe theory. Whilst I'm not an expert in either, I feel that at a bare minimum this article, which is concerned with the less known of the two, ought to explain why the two are different.--Leon (talk) 15:39, 16 September 2009 (UTC)[reply]

Seems like a good idea to me. Perhaps the best way to do it in this article would be to say that both catastrophe theory and chaos theory deal with physical systems where small changes in the parameters cause large changes in their behavior, but that catastrophe theory is limited to systems whose behavior is determined by a potential function in one of the forms given here. Robert O'Rourke (talk) 01:28, 26 March 2011 (UTC)[reply]

The crucial distinction between chaos theory and catastrophe theory is that chaos theory deals with changes in initial conditions, while bifurcation theory, which includes catastrophe theory, deals with changes in parameters. The logistic map is used in both chaos theory and bifurcation theory. Robert O'Rourke (talk) 20:34, 29 June 2014 (UTC)[reply]

Images

The svg images used in this page are pretty messed up; the legends have a lot of overlapping text. I'm viewing using: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.9.1.3) Gecko/20090824 Firefox/3.5.3 --75.90.223.53 (talk) 15:22, 8 October 2009 (UTC)[reply]

Thom's theorem

What's the name of the theorem which prove "If the potential function depends on two or fewer active variables, and four (resp. five) or fewer active parameters, then there are only seven (resp. eleven) generic structures for these bifurcation geometries"? It seems to be an important theorem but without seeing it we can't say it's cited. --虞海 (Yú Hǎi) (talk) 15:03, 3 November 2009 (UTC)[reply]

Is that "Thom's classification theorem"? --虞海 (Yú Hǎi) (talk) 15:10, 3 November 2009 (UTC)[reply]

Thats what Poston and Stewart call it.--Salix (talk): 19:23, 3 November 2009 (UTC)[reply]

Theory of Catastrophy is totally different area of study

Without understanding phase space and nonlinear system it is impossible to understand. Theory of Catastrophy is not a branch of bifurcation study. hopf bifurcation is also just one type of phase space shifting. therefore this article needs to be revised, may be rewrite. Theory of Catastrophy is totally different branch of nonlinear dynamics. germs of catastrophies and phase space shiftings are related to interactions between parameters and variables. —Preceding unsigned comment added by Galtbolor (talk • contribs) 04:23, 17 February 2010 (UTC)[reply]

This reference, removed from Bibliography, supports an alternative article:

Thompson, J. Michael T. (1982) Instabilities and Catastrophes in Science and Engineering New York: Wiley

This book may be available from Internet Archive. — Rgdboer (talk) 22:41, 3 July 2023 (UTC)[reply]

Congrats, you just stepped all over historical geographic catastrophic searching

Tried to do a quick lookup on the super volcano explosion at Lake Toba, and kept getting redirected to this instead.

Way to go Wiki editors. — Preceding unsigned comment added by 71.171.89.28 (talk) 07:52, 17 July 2014 (UTC)[reply]

How are you looking? A search for Lake Toba or Lake Toba volcano shows up Toba catastrophe theory among the first results. Diego (talk) 09:15, 17 July 2014 (UTC)[reply]

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