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Unformatted text preview: very straightForward. IF = 3 . 2 it is readily established that the series will, aFter a suFfcient time period, oscillate between two values: a 1 = . 799455 and a 2 = . 513045. This twocycle is typical oF the logistic equation For a certain range oF . To establish the range oF is straightForward but algebraically tedious. Here we shall give the gist oF the solution, and leave appendices 3.1 and 3.2 to illustrate how Mathematica and Maple , respectively, can be employed to solve the tedious algebra. Let f ( x ) = x (1 x ) then a twocycle result will occur iF a = f ( f ( a )) 9 We shall investigate chaos in chapter 7....
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 Fall '11
 Dr.Gwartney
 Economics

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