# Exercises for Chaos Under Control

## Chapter 4: Strange Attractors

34.[C] Select TENT/HISTOGRAM.

(a) Take s = 0.7. What is the attractor of the time series starting
with x_{0} = 0.5? What about x_{0} = 0.3 or x_{0} = 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 x_{0} = 0.5
different from that for other values of x_{0}? Explain.

(e) Compare histogram results with TENT/TIMESERIES.

35.[C] Select TENT/HISTOGRAM.

(a) For s = 1.2, compare the 1000-point histograms for x_{0} = 0.5 and
x_{0} = 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
x_{0} = 0.4 and x_{0} = 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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Return to Chapter 4 Exercises: The Butterfly Effect

Go to Chapter4 exercises:
The Family Portrait of Attractors

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