# Friday October 4

- Due Oct 7, 2019 by 11:30am
- Points 10
- Submitting a file upload

Use your logisticmap.py code to answer the following. Be sure to keep x0 in the interval 0 <= x0 <= 1.

1) What is the long-term behavior for 0 <= r <= 1? Does the behavior depend on x0?

2) Pick several values for r in the interval 1 < r <= 3 and report the corresponding equilibrium value (repeat of what we did in class). Hint: as you get closer to 3 you may need to increase T to see the limiting behavior. Does the behavior depend on x0?

3) Choose a few values for r in the interval 3 < r <= 3.44 and describe the long-term behavior (it should be qualitatively different from what we have seen before). Does the behavior depend on x0?

4) Pick several values for r in the interval 3.45 < r <= 3.54 and describe the long-term behavior (it should be qualitatively different from what you saw in (3)). Does the behavior depend on x0?

5) The change in behavior from the type of behavior in part (3) to the type of behavior in part (4) occurs at a specific r in the interval 3.44 < r < 3.45. Try to get one more decimal place of accuracy on where this change occurs. You may need to increase T again. Does the behavior depend on x0?