I recently came across Nonlinear Dynamics and Chaos by Strogatz and I'm recommending it to all my Physics/Applied Math friends. This is a great introductory book on the subject and you don't need any more Math than is taught in a basic Diff. Eq. course.
I love this book 'cause
a) Strogatz gives a simple but comprehensive Mathematical treatment of each topic and interprets the Math at each step. He actually shows you the intermediate steps with diagrams which encourages you to go on reading.
b) His examples involve applications (in Physics, Engineering, Biology, etc. etc.) that are quite often v. fascinating.