One-Dimensional Dynamical Systems

The idea is to have a personal copy of the package Chaos.mpl, which you can download here:

If you use Unix or Linux, you can start Maple from the directory in which you place this file. Then go ahead and type:

read(`Chaos.mpl`):

If you start Maple under windows, then the computer cannot easily find the Chaos.mpl package; you must specify the entire path where you saved this file. Hence, your command will look something like:

read(`M:/data/maple/Chaos.mpl`):

If you use a semi-colon when executing this Read command, you get more information about the procedures in the package. However, further instructions can be found at this site as well.

Especially when you wish to use the Chaos.mpl package with another dynamical system, you must always execute the above Read command first and then load a new system. You can choose from the following files:

Cosine.mpl
Cubic.mpl
Logistic.mpl
Quadratic.mpl
Quartic.mpl
Sine.mpl
Tent.mpl

The file Logistic.mpl contains the Logistic map, but this system is automatically defined when you start Chaos.mpl. Hence, if you first read in the file defining the dynamical system and then Chaos.mpl, the dynamical system gets overwritten by the Logistic map again!

The above dynamical system files must be read in by Maple in much the same way as the Chaos.mpl package, for example:

read(`Tent.mpl`);

Of course, as before, you must specify the entire path when working under Windows.

Chaos.mpl can plot orbits, show the graph of a map and its higher iterates, and compute the orbit diagram.