Talk:Bifurcation theory/Archive 1

Archive 1

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)

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)

Jacobian not square

According to the article, a local bifurcation occurs at (x0,lambda0) when the Jacobian there has a eigenvalue with zero real part, yet, if my understanding is right, the Jacobian isn't square, so it can't have eigenvalues. The Jacobian is (n+1)xn. Is this just a confusion of how I'm reading it, or is the article written wrong? --SurrealWarrior (talk) 16:58, 19 September 2008 (UTC) Perhaps the page on stability theory of nonlinear autonomous systems or the one about the jacobian matrx and determinant in dynamical systems can help further.

Examples from the natural sciences are relevant

Many math articles list examples. The exponential decay, exponential growth, and logarithm articles are examples of articles discussing fundamental mathematical ideas where discussion of examples of how these ideas are applied are included. There are many other examples of mathematical articles where discussion of examples of how these ideas are applied to real systems are deemed relevant and included. Citations showing how a mathematical idea is used to model a real system are sufficient to establish relevance. Why should the "bifurcation theory" article exclude examples of how the theory is used to model real systems? 140.32.16.101 (talk) 20:44, 11 August 2009 (UTC)

A real example (from PDEs, for example) of a simple example of a bifurcation would be relevant, although it still probably shouldn't be in the lead. An example of how one model of quantum chaos uses bifurcation theory should not be in this article. — Arthur Rubin (talk) 21:22, 11 August 2009 (UTC)

It appears that there are families of examples at the end of the #Local bifurcations section. — Arthur Rubin (talk) 21:38, 11 August 2009 (UTC)

You are guilty of edit warring by breaking the three revert rule.

There is a difference between a listing of types of bifurcations (pure math) and examples of applications of bifurcation theory to the natural sciences. There is tons of precedence in math articles for including brief references to applications of mathematical ideas to the natural sciences. Your claim that this article should exclude examples from the natural sciences is not supported by reason, common practice, or Wikipedia policy. The relevance of the example from the natural sciences is supported by several citations and a google scholar search for Gutzwiller AND bifurcation will bring up many more.

Wikipedia policies count for more than the opinion of a single editor. "Not notable" does not justify removal of material. Discussion of relevance should occur prior to multiple reversions removing sourced material. In general, citations justify inclusion of material unless there is an editorial consensus that they do not in a specific case. A single editor does not own an article and cannot rule by fiat that amounts to little more than "I don't like it." When an editor runs roughshod over established policies, that editor can be blocked. 140.32.16.101 (talk) 21:58, 11 August 2009 (UTC)

Nonsense. I have reverted 3 times, so I will not remove the material again, no matter that it doesn't belong in the article. However, quantum chaos is a mathematical theory describing the interaction of quantum mechanics and (macroscopic) chaos, so this isn't an "example of applications of mathematical ideas to the natural sciences". Period doubling for the (I can't remember the name of the differential equation describing a rigid pendulum) seems more appropriate, but still not in the lead.

And you've misread a number of policies.

1. The burden of proof for notability and relevance is always on the editor who wants the material added.
2. WP:LEAD provides that the lead should be a summary of the article. This implies to any credible observer that it does not include examples which are not further described in the body of the article.
3. WP:CONSENSUS suggests that a single, established, editor's opinion should be given more weight than a single, non-established, IP address. Your duty is to bring the matter to WP:3O, if you want it included.

— Arthur Rubin (talk) 22:15, 11 August 2009 (UTC)

I think the principle of one-way linking may be relevant here - establishing that bifurcation theory is relevant to some systems exhibiting quantum chaos does not establish that that system should be mentioned here. Additionally, Lead section states In general, the relative emphasis given to material in the lead should reflect its relative importance to the subject according to reliable sources. A single example not fully treated in the body clearly does not do this. Reserving the examples section for families of bifurcation with more specific examples treated at those articles would seem the best presentation of the topic at hand. I could, though, see an argument for mentioning the logistic map or some other system of historical importance to the study of bifurcation theory. - 2/0 (cont.) 15:12, 12 August 2009 (UTC)

Lots of math articles mention applications from physics in the lede, for example, "differential equations" and "Fourier series." I've added a section which provides a brief overview regarding bifurcations in semiclassical and quantum physics. The attention given to this class of examples is justified by the reliable sources cited.140.32.16.101 (talk) 15:57, 13 August 2009 (UTC)

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)

Hi, the animation is too fast and make it worthless... —Preceding unsigned comment added by Evolutioner (talk • contribs) 00:30, 27 February 2010 (UTC)

Relevance/weight of bifurcation theory in semiclassical/quantum physics

The repeated claim of irrelevance (and four reverts) of material that is supported with reliable sources needs better justification than editorial fiat. Examples of how mathematical theories are applied in the natural sciences are generally considered relevant, especially when supported with reliable sources. Support with reliable sources is prima facie evidence for relevance. Inclusion of examples from the natural sciences is standard encyclopedic practice in mathematics articles where such examples are available and documented with reliable sources. In light of these considerations, parties arguing for removal of material should explain their reasons why they maintain the material is irrelevant in spite of the sources provided. Since some degree of relevance between bifurcation theory and the material on semiclassical/quantum physics is clearly established with reliable sources, it seems that the real question is how much coverage is justified by the weight of the material. Therefore, I have added the appropriate tag to invite discussion. 140.32.16.101 (talk) 15:34, 14 August 2009 (UTC)

Your incorrect arguments from Wikipedia polices are getting tiresome. But I'm willing to leave it in this state for the moment.

As for your specific comments on this section, quantum chaos does not appear to be a "natural science"; it appears to involve a non-standard reading of quantum mechanics or of chaos theory. So applications to classical systems should probably dominate. — Arthur Rubin (talk) 16:12, 14 August 2009 (UTC)

I've supported the use of a "peacock" term for Gutzwiller's work with sources authored by independent scientists. Given the stature of Gutzwiller's work in the field, I am surprised the importance of his work was challenged. If over 2000 citations doesn't qualify a work as a "classic" in the field, then what does? The assertion that quantum chaos is not among the natural science borders on the absurd. How can one assert that an example is not from the natural sciences when the majority of cited works are from Physics journals and the cited works describe numerous experimental studies?140.32.16.101 (talk) 19:18, 17 August 2009 (UTC)

It was "fruitfully" that I was primarily disagreeing with, although "classic work" generally requires separate references. However, quantum chaos is clearly not among the natural sciences. At best, it's a method of explaining how quantum effects lead to (classical) physical chaos. It's still WP:UNDUE. — Arthur Rubin (talk) 19:44, 17 August 2009 (UTC)

Taken from the wiktionary:

"natural science (plural natural sciences)
  1. A science involved in studying phenomena or laws of the physical world; a general term of physics, chemistry, biology, astronomy, and so on."

I would pull the flag, this is easily within the definition.JascalX (talk) 05:46, 20 August 2010 (UTC)

The first fig changes too rapidly. —Preceding unsigned comment added by 70.107.78.242 (talk) 01:16, 11 October 2010 (UTC)

Chaos and Catastrophe as special cases of Bifurcation?

Bifurcation diagram of the Logistic map

According to J. Barkley Rosser in From Catastrophe to Chaos:A General Theory of Economic Discontinuities (Springer, 1991, p.3), "as with catastrophe theory, chaos theory is really a special case of the broader category of bifurcation theory." Not sure that an economics book is going to be a good guide, but is there in fact some connection between bifurcation and the other two theories? Chiswick Chap (talk) 16:17, 18 September 2015 (UTC)

I would have said that bifurcation theory is a special case of chaos theory. There is some connection. — Arthur Rubin (talk) 16:56, 18 September 2015 (UTC)

Ok, well perhaps it would be good if the article mentioned that and linked to it. All the best, Chiswick Chap (talk) 18:32, 18 September 2015 (UTC)

@Chiswick Chap: Similarly to User:Arthur Rubin, I would say that catastrophe theory is a special case of bifurcation theory, because catastophes are bifurcations; but chaos theory tends to be wider, because it encompasses both chaos itself and the cascades of bifurcations that can lead to it -- as in the classic bifurcation diagram of the logistic map, shown right. The study of individual bifurcations in this cascade would (IMO) be in the realm of bifurcation theory; they way they organise into a cascade leading to chaos would (IMO) be part of the broader subject of chaos theory. But others might have their own views. Jheald (talk) 19:58, 18 September 2015 (UTC)

Thank you, very interesting. That chimes with my non-mathematician's intuition. I think something of the sort should be stated in the article. Chiswick Chap (talk) 20:15, 18 September 2015 (UTC)