I'm just starting some research and I need a good introductory book in the topic of chaotic dynamics. Does anyone have a suggestion? Thanks.
You might want to specify about exactly what your background is and what you want to learn in order to get more effective answers. But given what you've asked for, I'd say the best place to learn about chaos and dynamical systems is absolutely: Steven Strogatz' Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering If you already know what's in this book, you need to rephrase the question; if you don't, this is what you need to know and where to learn it. Enjoy  I think this book is wonderful! 


Another introductory book worth looking at is An introduction to chaotic dynamical systems by Robert Devaney. 


It is a very popular topic and there are literally dozens of good textsa true embarass de richesse. One I like a lot is "Nonlinear Dynamics and Chaos" by Thompson and Stewart (Second Edition) a Wiley book. A book with the same title by Steve Strogatz is also very good, and so is Chaos: An Introduction to Dynamical Systems by Alligood, Sauer, and Yorke. If you are just getting started and want to get a feel for what it is all about, James Glieck's popular classic "Chaos" is a good place to begin. Good luck and have fun. It is a great topic full of interesting ideas. 


If you want to understand probability measures for dynamical systems, you'll probably want to learn about SinaiRuelleBowen measures in particular. A good introductory text accessible to undergraduates is Beck and Schlögl's Thermodynamics of chaotic systems. 


Here's a quick online find of a page about population dynamics and chaos in insects: http://home.comcast.net/~sharov/PopEcol/lec9/stabil.html It's by a theoretical biologist, Alexei Sharov, at the NIA. He also has other pages that could be of interest to you, including a summary of mathematical modeling of "forest insect dynamics": 

