Complimentary Microworld: Dynamical System Primer
Click the Hyperlink above to visit the Microworld in your Browser.
Author: Samad Mortabit

This Mathwright Microworld is an introduction to the basic ideas involved in the study of chaotic scalar discrete dynamical systems. This is done in an environment where exploring, reading, and writing all work together nicely. There is a brief mathematical discussion of the concepts involved (statement of definitions and some properties). It is not the intent of the author to develop those concepts here but rather design a workbook that allows for visualization and hands-on experiments. If the user is interested, we offer the following references:

[1] Robert L. Devaney, "An Introduction to Chaotic Dynamical Systems:, Addison-Wesley, 1989

[2] Denny Gullick, "Encounters With Chaos", McGraw Hill, 1992

[3] D. Assaf and S. Gadbois, "Definition of Chaos", American Mathematical Monthly 99 (1992) 865.

[4] J. Banks, J. Brooks, G. Cairns, G. Davis, and P. Stacey, "On Devaney's Definition of Chaos", American Mathematical Monthly 99 (1992) 332

[5] Carsten Knudsen, "Chaos Without Nonperiodicity", American Mathematical Monthly, (1994) 563

There are three kinds of pages in this 23 page Interactive Web Book.

  • Descriptive material giving background information and/or instruction about the interaction on a following page. This includes Windows Help that you may pop up on each page.
  • Interactive pages that give you the opportunity to explore hypotheses about discrete dynamics, and observe how these iterations go, step-by-step.
  • Exercise pages where you can practice what you have learned on the interactive pages.

Return to the listing of MathwrightWeb Microworlds

Once you download our free Mathwright32 Reader above, then simply click Get This Microworld, and it will be downloaded to your machine and installed in a directory there. You may find it whenever you want to view it, by going to the Start, Programs, Mathwright32 Reader menu.

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    - James E. White, Ph.D. , Library Director,
    author of this website, Mathwright 2000, MindScapes,
    MathwrightWeb, and Mathwright32

 

Mathwright Visualization Studio free Interactive Web Book:

Dynamical Systems Primer

Requires the MathwrightWeb or MathwrightNET ActiveX Control to read in your Browser.
For proper viewing, be sure to use Version 2.12 or later, dated Aug 14, 2003

 

 

This 23-page work, written in 1995 as a Mathwright WorkBook, was the substrate for a college-level course in discrete dynamics taught by the author. It exemplifies the goals of structured discovery learning so well that we have translated it essentially without change to our Microworld format so that you may view it either in your browser or offline. It is one of our new free Visualization Studio Interactive Web Books in the Math Cafe, and readers are invited to check it out before joining the Library to get a glimpse of what is possible with Mathwright.

This book also contains a "movie" that the user can generate, either online or off, that illustrates the "flip" and "tangent" bifurcations of the logistic map. At other places in the book, the reader may create cobweb diagrams using a bifurcation diagram (that she may also create for any dynamic she chooses) to select parameter values from the screen. The diagram below is an example.

 

The Microworld features a new capability of Mathwright (available since version 2.10, May 12, 2003) that makes use of Windows Compiled HTML Help to tell the mathematical story on each information page. These help pages use publisher quality formatted mathematical text and illustrations to tell their story. The activity pages offer the reader to experiment and to explore the properties of discrete systems at her own pace, and with her own questions.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


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For proper viewing, be sure to use Version 2.12 or later, dated Aug 14, 2003