Controlling Chaos on the Logistic Map

Consider the logistic map given by
, 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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S. Lynch, Dynamical Systems with Applications Using Mathematica, Boston: Birkhäuser, 2007.
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