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Controlling Chaos on the Logistic Map

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Consider the logistic map given by

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, where .

One method available to control the chaos in this one-dimensional system consists of applying periodic proportional pulses once every iterations ( when ). The number of fixed points is equal to . For a specific choice of , there are only a few values of that stabilize the logistic map. These ranges are restricted to , where .

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Contributed by: Housam Binous (March 2011)
Open content licensed under CC BY-NC-SA

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S. Lynch, Dynamical Systems with Applications Using Mathematica, Boston: Birkhäuser, 2007.

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