DSWeb Dynamical Systems Software aims to collect all available software on dynamical systems theory. This project was originally launched during the special year Emerging Applications of Dynamical Systems, 1997/1998, at the Institute for Mathematics and its Applications. The information here includes functionality, platforms, languages, references, and contacts.

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1D Maps

By James Meiss
1D Maps

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.

  • Maps
Software Type
  • Package
  • C++
  • MacOS
Compiled application available from http://amath.colorado.edu/faculty/jdm/1DMaps.html
Contact Person
James Meiss

Documents to download

Categories: Software

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