Homework 3



Homework 3: Due Thursday 15 April at the beginning of class

For all these problems, you will probably want to use the program at http://hornacek.coa.edu/dave/Chaos/orbits.html. If you prefer, you could use a spreadsheet program or a programmable calculator.

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

If you want, you may do this set of experiments with a partner, and hand in only one write-up. I'm mainly interested in seeing that you've explored the system thoroughly and made some semi-careful observations. This isn't meant to be a stressful ordeal.

Consider the following values for the parameter r:

  1. r = 0.5
  2. r = 1.5
  3. r = 2.8
  4. r = 3.2
  5. r = 3.5
  6. r = 3.56
  7. r = 3.835
  8. r = 4.00
For each of the parameter values, observe what happens to orbits of f(x). Consider only initial populations between 0 and 1. For each parameter value, you should:



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