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Example

It is interesting to use DynaSys to create the famous bifurcation diagram for the logistic map. You may do it as follows:

  1. In the equation dialog box, type two equations: x=mu*x*(1-x), and mu'=0. This causes DynaSys to see mu as a variable, but one that does not vary with time.
  2. DynaSys thinks there is a differential equation, so the default display is not for iterated maps. Delete the display you have, and create one for iterated maps. The variable mu should be on the horizontal axis, and x should be on the vertical. The display rectangle should be (0,4)x(0,1).
  3. DynaSys also assigned a differential equation solver by default. Select the Algorithm item from the Numerics menu, and choose the Iterated Map solver.
  4. Select the Algorithm Controls item from the Numerics menu, and set the number of iterations to ignore to 100, and the number of iterations to plot to e.g. 50.
  5. Values for the parameter mu are now set by clicking the display using the right mouse button, since mu is a considered to be a variable. Double-click with the right mouse button to see the equilibrium points for values of mu less than 3, and the periodic and eventually chaotic orbits that take place for mu > 3.

Kevin Cooper
Wed Sep 30 15:21:52 PDT 1998