Talk:Bifurcation theory

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WikiProject Mathematics     (Rated B-Class) Mathematics Portal This article is within the scope of WikiProject Mathematics, which collaborates on articles related to mathematics. Mathematics rating: B Class Mid Priority  Field: Applied mathematics Please update this rating as the article progresses, or if the rating is inaccurate. Please add to or update the comments to suggest improvements to the article. Can be made more accessible. Add short descriptions of the bifurcations; normal form theory. Perhaps importance should be high. -- Jitse Niesen (talk) 12:30, 24 May 2007 (UTC) WikiProject Physics      (Rated B-Class) Portal This article is within the scope of WikiProject Physics, which collaborates on articles related to physics. B This article has been rated as B-Class on the assessment scale. High This article is on a subject of high importance within physics. Help with this template Comments: edit – history – watch – refresh Can be made more accessible. Add short descriptions of the bifurcations; normal form theory. Perhaps importance should be high. -- Jitse Niesen (talk) 12:30, 24 May 2007 (UTC) WikiProject Systems     (Rated B-Class) Systems science Portal This article is within the scope of WikiProject Systems, which collaborates on articles related to Systems science. Systems rating: B Class High importance  Field: Dynamical systems Please update this rating as the article progresses, or if the rating is inaccurate. Please add to or update the comments to suggest improvements to the article. Can be made more accessible. Add short descriptions of the bifurcations; normal form theory. Perhaps importance should be high. -- Jitse Niesen (talk) 12:30, 24 May 2007 (UTC)
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Wikipedia lacks entries on "Center manifold theorem" and "transformation to normal form" --Anonymous

[edit] Lets make the article A-Class

Let us make a concerted effort to make this article A-Class as soon as we can. Here is list of topics working on which should lead to improvement in the quality of the article:

1. Making the language more rigorous: There are several statements in the article that are not mathematically precise. While such statements are make the article more readable at times, but I think that in this case many need to be re-written. Consider, for example, the first line of the article: "a bifurcation occurs when a small smooth change made to the parameter". This statement means that there can indeed be a non-smooth small change in a parameter, which is incorrect. Later in the article there are claims to the effect that all bifurcations are related to eigenvalues crossing the imaginary axis, which is not true (flip bifurcation or global bifurcations being counter examples). Also, not all global bifurcations occur due to "collision" of two objects in the phase-space. In short, there are many language and detail related changes that need to be made.
2. More "coverage" required: Presently the article does not cover many important topics in bifurcation theory. Here is an incomplete list of topics that need to be included:

• Theory of normal forms
• Center manifold theory
• Bifurcation diagrams
• Poincare maps
• Perturbation methods (near critical points)
• Method of multiple scales (near critical points)
• Bifurcation of DAEs and related phenomena
• Examples and diagrams for each kind of bifurcation
• Computational aspects of bifurcation theory
• Discussion of software tools like AUTO, MatCont, Content, BifPack, PyCont etc

NOTE: This section is under active development. Please contribute to it and the main article.

[edit] Bifurcation Theory template

Anyone here good with wiki templates/footers? Thought it would be a good idea to create a template for the common bifurcation articles, and bifurcation theory in general, rather than cluttering the 'see also' section for all of them. I'll see what I can whip up...feedback welcome! Good idea/bad idea? jugander (t) 12:53, 17 October 2006 (UTC)

I am not sure a bifurcation template is useful. Can you provide a more detailed example how such a template would unclutter an article ? I might also add I consider templates (navigational templates) in most cases not helpful. So before you do any serious editing please present you template here. Having said this I think the dynamical systems articles in wikipedia are not in good shape so any improvement is appreciated. MathMartin 12:09, 18 October 2006 (UTC)

Here are two versions of what I've chosen out, one verbose, one less verbose. I thought to do this instead of cluttering all the "see also" sections of the bifurcation articles. I personally find navigational templates very useful when done well, notably Template:ProbDistributions for a good interlinking of probability distributions.

The top version is what I consider the most-possibly verbose version, i tried to collect everything related I could think of, and it probably shouldn't be used. The second version is shaved down to what I think is a good size.

Also, I'm writing an infinite-period bifurcation stub real soon (Update: done). Neimark I haven't studied, so that will have to remain red unless someone else can pitch in. It would be fun to see the homoclinic/heteroclinic maths articles cleaned up generally, it's on my 'maybe eventually' list. But getting back to the template, what are the opinions? jugander (t) 21:44, 18 October 2006 (UTC)

[edit] Organizing bifurcation theory

F y'alls I, I decided to make redirects from local bifurcation(s) and global bifurcation(s) to this main Bifurcation theory page. I started to write a new article mostly copied from this one, but decided against it, thinking it would be better to concentrate efforts. jugander (t) 22:16, 18 October 2006 (UTC)

[edit] Animation speed

I think it could do with slowing down by factor of 2 or 3! 8-)--Light current 23:54, 13 November 2006 (UTC)