Four examples of the displays from 1DMaps.

I use this program as a teaching tool for both undergraduate and graduate dynamical systems classes. It can be used for demonstrations as well as labs.

1DMaps is a Macintosh application for displaying the dynamics of some one-parameter families of one-dimensional, discrete dynamical systems. The program contains seven different maps, including the standard logistic map. One can plot five different representations of the dynamics:

• cobweb diagram,
• "Poor man's" bifurcation diagram, showing attracting orbits
• Lyapunov exponents;
• Invariant density, a histogram computed for an orbit of a fixed length; and
• Escape time, for example for the Logistic map with r>4.

The user can interact with each of these windows. For example new initial conditions can be selected with the mouse, and iterations done step-by-step with the space bar. One can zoom-in to smaller structures by dragging over the region to be enlarged.

This program is regularly used by the author as a demonstration in classes, for example for the undergraduate "chaos" class, APPM 3010, at the University of Colorado. Students also get hands on experience in a short lab. A short tutorial is on the DSWeb Tutorials site. The lab is contained in the attached pdf file.