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

- 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. - 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). - DynaSys also assigned a differential equation solver by default.
Select the
**Algorithm**item from the**Numerics**menu, and choose the Iterated Map solver. - 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. - 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`.

Wed Sep 30 15:21:52 PDT 1998