Exercises for Chaos Under Control

Chapter 4: Strange Attractors


(a) Take s = 0.7. What is the attractor of the time series starting with x0 = 0.5? What about x0 = 0.3 or x0 = 0.9?

(b) Repeat part (a) for s = 1.

(c) Repeat part (a) for s = 1.5.

(d) Repeat part (a) for s = 2. Is the attractor for x0 = 0.5 different from that for other values of x0? Explain.

(e) Compare histogram results with TENT/TIMESERIES.


(a) For s = 1.2, compare the 1000-point histograms for x0 = 0.5 and x0 = 0.9.

(b) Repeat part (a) for s = 1.4, s = 1.6, and s = 1.8.

(c) Recalling exercise 29, what can you say about the histograms for x0 = 0.4 and x0 = 0.6?

36.[W] Historians are frequently confronted with the task of trying to assign cause and effect relations to seemingly random occurrences. How might the ideas of deterministic chaos alter the discipline of human history?

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