Wow, did we make it this far? That was probably way too much material in far too short a time (and if so, let me know). Nevertheless, if you picked up the following concepts you are way ahead of the game.

- You haven't finished a model until you've understood it
- It is often possible to understand the global behavior of low-dimensional dynamical systems by viewing their behavior in phase space.
- By mapping out the fixed points and attractors, we can get an intuitive understanding of how small changes in our system will effect the outcome.
- Low dimensional chaos is still understandable and predictable.
The important measure is how much
*can*your predict. - In some non-linear systems small changes can change the stability of the whole system. We need to understand how resilient, our much more complicated system is to various kinds of forcing.

Mon Sep 22 21:30:22 EDT 1997