Talk:Bifurcation theory

Untitled

Wikipedia lacks entries on "Center manifold theorem" and "transformation to normal form" --Anonymous

Ok... ElectroChip123 (talk) 00:32, 25 March 2019 (UTC)

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.

- - -

• Well, not to rain on anyone's parade, but -- alas -- the concept of "A-Class" presupposes a specific 'class' with respect to the audience's level of education & specialization. Already, even within the above request, Wikipedia mathematics articles in general slip almost unconsciously, almost always, into inaccessible jargon. This is not just an affliction of Wikipedia, by the way: MOST mathematicians can't access most math journal articles. Fact...and it is due to specialization within mathematics. If I could wave a magic wand and fix the problem (regrettably, I cannot) it would be to create a CAUTION label for *all* math articles on Wikipedia that reminds editors that all articles -- even mathematical -- can, should and must be written at the 7th grade reading level...just as "real" encyclopedias are. As regards opinions on this apparently intractable problem, "Your mileage may vary." Be well...and be honest (we all need you to be as such...and so do you). --104.15.130.191 (talk) 19:19, 14 June 2020 (UTC)

Assessment comment

The comment(s) below were originally left at Talk:Bifurcation theory/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

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)

Last edited at 12:30, 24 May 2007 (UTC). Substituted at 09:36, 29 April 2016 (UTC)

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Proposed Merger

The articles on Indefinite-period, homoclinic, and heteroclinic bifurcation are all stubs. The information in them can easily be fit into this article by expanding the Global bifurcations section. Furthermore, this merge will improve the quality this article by adding more information and more sources to it. ElectroChip123 (talk) 00:29, 25 March 2019 (UTC)

  Y Merger complete. Klbrain (talk) 07:31, 25 April 2020 (UTC)

Motif

I deleted this claim from the lede:

"Henri Poincaré also later named various types of stationary points and classified them with motif."

Motive (algebraic geometry) appears to offer an explanation of what a "motif" is. But it seems to be a branch of maths that was developed after Poincaré's time. I can't find anything that links Poincaré with motifs. The claim is in the lede, which is supposed to be a summary of content in the main body; but this claim isn't a summary of anything in the body.

I'm not a mathematician, and I can't understand what I've read about motives/motifs.

MrDemeanour (talk) 08:51, 26 July 2023 (UTC)