Bifurcation Diagram: Initial Exploration



You should complete these exercises by the beginning of our class on Friday September 17. Feel free to work in pairs if you wish.

As before, this is isn't an official homework; there's no need for a fancy write-up. But you should have some notes to hand in. I'm not going to evaluate this, I just want to see what you've found and check off that you did it. I expect that doing these will take around half an hour.

For all these problems, you will probably want to use the program at http://hornacek.coa.edu/dave/Chaos/bifurcation.html. This is the program I showed you in class.

All of the questions below concern the logistic equation, f(x) = rx(1-x). You will explore what happens when you iterate of f(x), for different values of the growth rate r.

  1. Appreciation: Make some bifurcation diagrams and admire them. Zoom in in different areas. What do you notice?

  2. Exploration: Find a parameter value for which the logistic map is period 5. Find an r value for which the logistic map is chaotic. Find an r value for which the logistic map has a period greater than 10.


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