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.

Please note that DSWeb is not responsible for any direct, indirect, special, incidental, or consequential damages arising from the use of the content provided here.

1D Maps

Iterate one dimensional maps, displaying cobweb diagrams, bifurcation diagrams, Lyapunov exponents, invariant densities, and escape times

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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.

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

Documents to download

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