Proffesor Strogatz wrote a book called Ninlinear Dynamics and Chaos which is the best intro book on non linear diff eq I have ever come across. I highly recomenend it: https://www.amazon.com/Nonlinear-Dynamics-Chaos-Applications...

As someone whose spent way too long and way too much time in over my head with non linear systems ( this area has been trendy and fruitful in the quantitative finance community since hte late 90's) I can second the post's book recommendation....

http://www.amazon.com/Nonlinear-Dynamics-And-Chaos-Applicati...

In fact everything by that author is great, buy and read it all:)

http://www.amazon.com/Steven-H.-Strogatz/e/B001KHB290/ref=dp...

Just make sure you've read up on your differential equations before you start:) This isn't a topic for someone without a strong background in the mathematics!

Unfortunately I have yet to find a good introductory course, video, book, pdf....anything for this topic. I had to jump in with a specific model in mind and keep banging away until I iterated my way towards the solution.

Suggestions for introductory material are welcome!!!