Okay, if we've survived through the first two labs we should have a
much better feel for the concepts of phase-space, fixed points and
stability of dynamical systems. However, we still haven't seen any
chaos. As it turns out, I wasn't being nice, it just happens to be
impossible to get chaos with less than three
variables
.
However, with three variables, things can get very interesting indeed. Here we will explore one of the classic systems that display chaotic behavior in three variables: the Lorenz Equations, which were explored (and explained) by Edward Lorenz in his phenomenal 1963 paper [7] ten years before Chaos was ``discovered''. Gleick [1] presents this story very nicely. Here we will delve into the quantitative aspects of chaos a bit more deeply using the tools we have already developed. When we are done I hope you will have a better understanding of