Unformatted text preview: very straightForward. IF Î» = 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 Î» . To establish the range oF Î» 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 ) = Î» x (1 âˆ’ 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, Chaos Theory, Economic Dynamics, sufficient time period, Simple recursive formulation, possible chaotic behaviour.9

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