Talk:Bifurcation diagram

message: The article claims that it is customary to show the unstable solutions as dotted lines, however the image is missing a number of unstable solutions (namely (r-1)/r). Can it be added please?  — Preceding unsigned comment added by 68.173.18.226 (talk) 15:22, 4 September 2011 (UTC)
thread_title: unstable solutions

message: I have deleted most of this text since it was about the logistic map or about the mandelbrot set, but not about bifurcation diagrams and most of its contents was already contained under logistic map. I am not an expert on dynamical systems, so I hope someone else can write the appropriate article for this title.
--Lenthe 16:29, 17 Jun 2005 (UTC)
replies: text: An important theorem about bifurcation diagrams is Sarkovskii's theorem, summarized as "Period three implies chaos". 
Sarkovskii's theorem is not about bifurcation diagrams, since it doesn't say anything about how the cycle structure changes as the parameter is varied. Also "Period three implies chaos" is not Sarkovskii's theorem, and does not follow from it. AxelBoldt 02:17 Sep 30, 2002 (UTC)
The order in which the cycles first appear, starting with the 1-cycle and ending with the 3-cycle, is the same as Sarkovskii's order backward. "Period Three Implies Chaos" is by James Yorke. I haven't read it, but according to Chaos by James Gleick, when Yorke was in Berlin, Sarkovskii came up to him and told him that he had proved the same result. -phma
The diagram shown here is not a bifurcation diagram.  It is an orbit diagram (which is unfortunately sometimes incorrectly referred to as a bifurcation diagram).  A bifurcation diagram shows all cycles, attracting or otherwise, and does not include points that have not yet converged to a cycle, since it is not generated by iteration.  I know of a good reference that explains the difference and has examples of both.  I will try to find it. CyborgTosser (Only half the battle) 09:05, 26 Apr 2005 (UTC)
thread_title:  Deleted 

message: I'm going to try and attempt to rewrite this page, as currently it's not really about bifurcation diagrams per se. If anyone has any comments or would like to help, that would be great. Mathmoclaire 13:19, 29 July 2006 (UTC)
thread_title: Rewrite

message: The one on the top is better because it uses more iterations for every value of the parameter r; it then uses shades of grey to indicate which regions are visited most frequently. The picture is also bigger. On the other hand, the description of the bottom picture has some Octave code which may be useful. -- Jitse Niesen (talk) 03:12, 19 April 2007 (UTC)
replies: text: It would be nice if the first one had source code...   I don't understand the obsession with deleting all unused images ASAP. — Omegatron 14:47, 19 April 2007 (UTC)
thread_title:  Which image is better? 

message: Please add some!Lakinekaki 21:11, 19 April 2007 (UTC)
thread_title:  external links and references missing 

message: 3.739 is P5. The edge of chaos where order is to the left and chaos is to the right is greater than 3.74432 but equal or less than 3.74433. -32ieww 10:09PM 11/19/2015 NY time  32ieww (talk) 03:09, 20 November 2015 (UTC)
thread_title:  Edge of chaos