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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.

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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 re-phrase 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!

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specifically I will be applying chaotic dynamics to modeling population distributions. I think this book will be a good introduction to the topic though. Thanks – Aaron Sep 18 '10 at 7:12
@Aaron, you might want to edit your question at the top of the page to include your comment about your interests, just in case someone tries to answer your question without reading the full page. They might not notice the detail about your interest in population distributions. – sleepless in beantown Sep 19 '10 at 0:13

Another introductory book worth looking at is

An introduction to chaotic dynamical systems by Robert Devaney.

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It is a very popular topic and there are literally dozens of good texts---a 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.

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

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Here's a quick on-line find of a page about population dynamics and chaos in insects:

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":

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