Talk:Catastrophe theory

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[edit] 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)

[edit] 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)

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)

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)