Day 5
5 March 1998
Dynamics of Complex Systems
Summary of this Day's Class
Once again I have included the transparencies below in Word 97, ps and pdf formats.
There are a few figues that I put in while photocopying. If you would like complete transparencies please email me.
Dynamics-1.pdf - PDF Format, 87 kb.
Dynamics-1.doc - Word 97 Format, 145 kb.
Dynamics-1.ps - Postscript Format, 448 kb.
Today's class dealt with nonlinear dynamics of maps - mainly the logistic equation.
We discussed the concept of a map, fixed points, stability of fixed points, attracting fixed points, repelling fixed points, and bifurcations.
The Serendip web site has a Java Script Cobwebbing Applet with a nice tutorial.
Go to Our Nonlinear Dynamics Links.
Or see JAVA applets for chaos and fractals from the Dynamical Systems and Technology Project at Boston University, directed by Robert Devaney
Also look at software created by Robert Devaney.
Also I found a site where one can download software for making fractals and playing with chaos:
Sprott's Chaos and Fractal Software by J.C. Sprott
No Homework Assignment this week
Reading Assignment - Read the articles by 11 March 98
Gardner, Martin. 1978. Mathematical Games: White and brown music, fractal curves and one-over-f fluctuations, Scientific American, April 1978, 238:16-32.
Bak, Per, and Chen, Kan. 1991. Self-organized criticality, Scientific American, January 1991, pp. 46-53.
Bak, Per. 1996, How Nature Works, Copernicus: Springer-Verlag, NY, Chapter 1, pp. 1-32.
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