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An Introduction to Dynamical Systems and Chaos
Marc Spiegelman, LDEO
September 22, 1997
This tutorial will develop the basic ingredients necessary for
modeling and understanding simple (and not so simple)
non-linear dynamical systems. The goal of these exercises are to
demonstrate you that you can develop significant insight into the
behavior of complicated non-linear systems with just a little math, a
little art and a little modeling software. By themselves, these tools
can lead to frustration. However, when combined in the right ways
they can give you surprising powers of understanding. The purpose of
this tutorial is to give you practice and guidance into the basic
tricks of the trade so that when you are done you will be able to
- Recognize a dynamical system when you see one.
- Visualize the behavior of the entire system with just a few
tricks
- Solve specific instances using STELLA
- Understand a systems fixed points and stability
- Be happy in phase space
- Get a taste of real Chaos
This module contains three labs of increasing complexity that try to
highlight the important concepts of non-linear systems while
developing enough basic tools to be useful. However, these labs are
only a brief introduction to a rich and extensive subject. For a
beautiful but qualitative overview of the subject see Gleick [1].
Then read Strogatz [2] for an excellent introduction to
the quantitative guts of the business.
Postscript or PDF versions of Tutorial are here
marc spiegelman
Mon Sep 22 21:30:22 EDT 1997
