Summary and Conclusions

 

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.