for an explanation of the software and sample lab assignment using it.
One-dimensional maps are the simplest dynamical systems that may be chaotic. Textbooks can give a static picture of such dynamics, but since dynamics involves time, a student can get a much better understanding of evolution and chaos by using hands on software. There is no substitute for seeing dynamics evolve before your eyes. While there are many general purpose tools that can be programmed to show these dynamics, having a single purpose application allows the instructor and the student to focus on the phenomena, avoiding the programming details.
James Meiss developed and has used the Macintosh application “1DMaps” in both in an undergraduate engineering focused course on dynamics (usually using Steve Strogatz’s wonderful text), and in a graduate course on discrete dynamical systems. Randell Callahan was a student in the undergraduate class last fall, and has been porting the 1DMaps program to iOS so it will run on the iPad, and iPhone platforms.
Goals of the lectures, labs and homework assignments that use 1DMaps are (1) to develop an intuition for how one iterates maps (2) visualize the concepts of stability, bifurcation, and asymptotic behavior, and (3) investigate Feigenbaum’s universality.
|Author Institutional Affiliation
James Meiss and Randell Callahan