This was a great introduction to the subject. It turns out nonlinear systems are everywhere. Engineers have fooled ourselves by linearizing things for so long. We've basically pretended nonlinear responses are linear, so that we can deal with them. It turns out there is some extremely surprising and interesting behavior which is predictable in a general way, even if unpredictable in an exact way, that we've overlooked up to the last decade or so when Chaos as a science began to yield so many interesting results.
It's really important to understand the whole butterfly effect thing, that even very simple and well-defined nonlinear systems have long term behavior that's basically unpredictable because even miniscule differences in initial conditions (differences too tiny for us to measure) can quickly snowball into large scale macro phenomena. It's one reason why the future is unknowable (in our current understanding of physics.)