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Bifurcation Diagram, quick help please

  1. May 25, 2005 #1

    Zurtex

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    Could some explain or point me to somewhere explains what a Bifurcation Diagram is and how to draw one given a non-linear function. Got an exam today and nobody knows what one is. If it has already been 2 hours after I've posted this don't worry, I'll be heading off to the exam hehe. Thanks if anyone can give any help.
     
  2. jcsd
  3. May 25, 2005 #2

    Zurtex

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    Too late now, thanks if anyone tried to look something up.
     
  4. Jun 4, 2005 #3

    saltydog

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    Jesus Zurtex. I'm a day late and a dollar short, alright 5 whatever. Wish I would have seen this but I was away for awhile. Has a bifurcation diagram ever been presented in the forum? You know it's one of the three icons of Chaos Theory right? You know, Mandelbrot Set, Lorenz attractor, Feigenbaum plot (bifurcation diagram). We should post one. Well me if you don't feel like it. In fact, since we have three spaces down there, we should post all three. Dude, you're long gone with this aren't you.
     
  5. Jun 5, 2005 #4

    saltydog

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    Attached is the bifurcation diagram for the logistics map. You can make a much more detailed one using C++ but I can't convert it to JPEG so I have to use Mathematica.

    [tex]x_{n+1}=kx_n(1-x_n)[/tex]

    I suppose it is relevant to differential equations since bifurcation diagrams can also be created for differential equations (pretty sure anyway, need to check). Zurtex, wanna' generate one for such? I suspect I know what you're thinking, "dude, I ain't generating nothin', it's summer time". :smile:
     

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