Question: all questions Figure 2 A cobweb diagram for f(x) = 3.55x(1 x) is presented here. The sequence of values results in an 8 -cycle. 1.

all questions Figure 2 A cobweb diagram for f(x) = 3.55x(1 x) is presented here. The sequence of values results in an 8 -cycle. 1. Let r = 0.5 and choose x0 = 0.2. Either by hand or by using a computer, calculate the first 10 values in the sequence. Does the sequence appear to converge? If so, to what value? Does it result in a cycle? If so, what kind of cycle (for example, 2 cycle, 4 cycle.)? 2. What happens when r = 2? 3. For r = 3.2 and r = 3.5, calculate the first 100 sequence values. Generate a cobweb diagram for each iterative process. (Several free applets are available online that generate cobweb diagrams for the logistic map.) What is the long-term behavior in each of these cases? 4. Now let r = 4. Calculate the first 100 sequence values and generate a cobweb diagram. What is the longterm behavior in this case? 5. Repeat the process for r = 4, but let x0 = 0.201. How does this behavior compare with the behavior for x0 = 0.2?

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