Part of June 22, 2010 Handout

SIMPLY CHAOTIC *

We do not need to go to something as complicated as weather prediction to find chaotic behavior. The simple equation x[n+1] = r*x[n]*(1-x[n]) ('*' stands for multiplication) exhibits chaotic behavior for r equal to 4. (You can find a discussion about the origin of this equation and several of its properties in pp. 69-80 of the book Chaos - Making a New Science by James Gleick, New York, Viking, 1987). The following three plots show how the values of x diverge, even when at the start are nearly identical.

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