The Logistic Map Fixed Points Model finds periodic trajectories of the logistic map such that n iterations of the map starting with an initial value x return to that value.  The key idea for this model is that for values of the logistic map control parameter r in the chaotic regime, there are periodic but unstable trajectories. This property of the chaotic regime means that if we choose the value of the seed x0 to be precisely equal to a point on an unstable trajectory with period n, the subsequent trajectory will have this period. However, if we choose a value of x0 that differs ever so slightly from this special value, the trajectory will not be periodic.  This model shows how to find these special values of x0.

The Logistic Map Fixed Points Model was created using the Easy Java Simulations (EJS) modeling tool.  It is distributed as a ready-to-run (compiled) Java archive.  Double clicking the ejs_chaos_LogisticMapFixedPoints.jar file will run the program if Java is installed.

Please note that this resource requires at least version 1.6 of Java.