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Poincare section and bifurcation diagram

  1. Apr 15, 2008 #1
    1. The problem statement, all variables and given/known data

    This is the bouncing ball experiment, a circuit is used as an analog of a ball bouncing on an oscillating table. The amplitude of the tables oscillations is varied and data representing the balls position and velocity is gathered.

    I have to plot a poincare section for when the ball is bouncing with a single period, another once period doubling is observed and another once it goes to chaos. Then I have to plot a bifurcation diagram.

    I know from my phase-space maps that my data is good and that I have actually observed period doubling and chaos


    2. Relevant equations

    None

    3. The attempt at a solution

    I have read every book in my university library on the subject and have been trawling the web for hours, I can find plenty of poincare sections and bifurcation diagrams but nothing about how to extract the data which needs to be plotted.

    It was explained to me that for the poincare section a sample is taken of the ball velocity and ball position for a given table position, and the two plotted against each other. Then another sample is taken exactly one period of the tables osciallation later. This means that for single periodic motion of the ball the poincare section is only one point, then after period doubling it is two points and so on. However every poincare section I can find in a book or in a paper is a whole series of points and not just one. I was also told by our lab supervisor that the bifurcation diagram is just all the poincare sections added together but I don't think that it right.

    Please tell me what I need to plot for the poincare section and bifurcation diagram!
     
  2. jcsd
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