1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Continuous Logistic Map

  1. Feb 12, 2006 #1
  2. jcsd
  3. Feb 13, 2006 #2


    User Avatar
    Science Advisor

    The corresponding continuous system would be.
    [tex]\frac{dx}{dt}= rx(1- x)[/tex]
    where x is a continuous function of t.
  4. Feb 13, 2006 #3


    User Avatar
    Science Advisor
    Homework Helper

    I wish to clarify something: The continuous counterpart of the logistic equation is not chaotic. It turns out that in order to find chaos in continuous systems, we need to consider at least a three-dimensional system. Such as the Rossler System:




    or the Lorenz system.

    Hey Tom, have you ever studied these two systems? Have you drawn a Feigenbaum plot for either? I hope you have Peitgen's book, "Chaos and Fractals". That's a good reference.
  5. Feb 14, 2006 #4
    The "translation" I got is;
    dx/dt = 0
    dy/dt = 1
    (Do you think they are too simple?) Although the solution of above differential equations is a line in two dimensional Euclidean space, the solution in the following quotient space;
    is thought to have chaotic behaviour.
  6. Feb 14, 2006 #5


    User Avatar
    Science Advisor
    Homework Helper

    Yep, yep, that's not happening for me. When in doubt . . . Mathworld . . . Quotient Space . . . still didn't happen for me. You got me Tom. And that diagram your cited, what is that? Anyway, I'm not clear at all what a quotient space is and how it can model chaotic behavior. Might you provide a concrete example with pictures. Yea, pictures . . . that would be nice.:rolleyes:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook