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...
Starting out with the basics of state-space representations, it moves from 1D to 2D to 3D dynamics. The last section deals with the popular topics of chaos theory and fractals. But not from a simple pop-math perspective that you'll find in the math section of the book store. It's the real deal, except presented in a way that can be understood by non-mathematicians.
Strogatz is also coauthor of the paper that introduced small world networks. I really admire him for being so brilliant and at the same time capable of getting these topics across to everybody. I also recommend his book Sync.