Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering (Studies in Nonlinearity)

This book was the textbook in a course on nonlinear dynamics that I took. The course covered most of chapters 2-8 (chapter 1 is an introduction and is very short), so please consider my comments from that context. Speaking personally as an individual student- I tend to rely very heavily on my textbooks for learning and generally read them deeply. This book was no exception.Overwhelmingly, the great strength of this book is the quality of the writing style. This is a very rare math book in that it is actually fun to read. The examples are for the most part very good- easy to follow and understand. The author focuses a lot on the big picture perspective of the techniques involved and does a superb job of developing a very good intuition and feel for nonlinear systems. In fact, the prose is so readable, I would not have any hesitation recommending this book for someone wanting to teach them self the topic (assuming the necessary background of course). I feel that this book could easily accommodate such a student.Another great strength of this book is the way that ideas build upon one another. The author has masterfully written a book in which your intuition about early concepts pave the way for understanding later concepts even though missing some ideas in the beginning will not cripple you in later chapters. (IE, in many books if you do not understand chapter 1, you will fail in chapter 2, etc...)The problems are very doable, but yet seem to capture the essence of ideas in the chapters well. This is in contrast to many books in which the easy problems are practically busy work, and the problems that teach you something require you to saw off your left foot. The author strikes a nice balance here. Another nice feature is that the author draws actual models from a broad range of disciplines to build the practice problem sets and worked examples.The only real complaint I have about this book (as a pure math guy), is that this book is VERY skimpy on the theory(as in proofs and connection with deeper ideas)- but I think this book is targeted to a non-mathematics or an applied math audience. Personally, I found this frustrating and somewhat unsatisfying, but consider the nature of the class/audience. The author does sprinkle some theory around, such as the occasional reference to Topology and a section on index theory- but don't blink, you might miss it. The author rarely provides proof for theorems, those that he does provide are generally very simple and seem to be provided for their intuitive value rather than rigorous completeness. I considered giving it 4 stars instead of 5 due to the lack of rigor, but both considering its intended audience and its effectiveness at building intuition dismissed that consideration quickly. If you are looking for a book that digs into the theory, this is definitely not the book for you- at least not as a primary reference.Another minor shortcoming (not so much a short coming as quality which is lacking which could make this book better) is that the book provides practice problems for use on a computer(appropriately) but does not provide any example code at all. This is not a big deal, a quick google search could easily provide you with a basic demonstration of the syntax necessary to plot a system using the language of your choice, but still. Personally, I would not let such a thing be a deal breaker for this book. (At least the author has not taken the other extreme and written the book entirely around one particular proprietary language!)Despite these shortcomings, I strongly recommend this book either as a primary text for a course in nonlinear dynamics targeted to a non-pure-math audience, or as a secondary reference for anyone. I think this is a great book that will serve you well!Oh, if the author is reading this post-ADD MORE COLOR PICTURES OF CHAOTIC SYSTEMS PLEASE!! I love looking at those!

Book arrived in excellent quality - practically brand new - at expected time. Solid introduction to non linear dynamics and chaos theory; although I am a math major my prior experience in the field was limited to basic ODEs. The book is written in an accessible style without the stilted definition-theorem-proof form of other textbooks, but has a rigorous treatment of the subject. Dizzying array of scientific and engineering applications. Overall strongly recommend!

It is rare that books of this type are both comprehensive and readable. Strogatz has managed to cover a wide range of concepts in significant detail while providing examples to illustrate his major points.The beginning of the text starts of with one dimensional nonlinear systems of first order (like the logistic equation), and Strogatz outlines the typical framework that one uses to analyze such systems. He defines fixed points, illustrates and defines bifurcations, and solidifies every claim with good examples.The text eventually moves to higher order systems with coupled or non-coupled sets of differential equations. For the most part, exercises for the student involve sets of two differential equations that can be linearized using Jacobian methods.Later, Strogatz provides a nicely executed description of fractals and fractal dimension, using examples from the Cantor set and the von Koch curve.The beauty of the book is that it is well written and complete. It even provides some limited solutions to selected exercises in the back. The examples in the book cover a wide range of areas. Mechanical oscillating systems like a mass on a spring, electrical circuits that follow the same equations, laser models that follow a modified logistic equation, and many variations of the Lotka-Volterra model are outlined through examples in the text.The book is a stand-alone text, equally useful as a textbook for an intorductory course or as a reference for someone merely surveying the subject. It deserves the highest rating possible.Edit: 2/28/07Now with a few years of hindsight, I would say this might have been the best stand alone textbook I had in grad school. This was one of the few books I had where I could teach myself the subject matter by just reading it. It is a great book that takes the mysticism out of a new and growing field.

This is probably the best math book I've ever read. Unlike other stuffy books, this one is very personable and informal. It is extremely readable, the explanations are crystal-clear and very intuitive and well-motivated, plus the author inserts a lot of humor (it's so nice to be reminded that mathematicians are humans). There are fascinating examples culled from applications.I should note two things. First, it is not a proof-based book. It discuesses the cool theorems and gives intuitive justifications, but the author is clear that his goal is to build intuition and give experience with the techniques, rather than mathematical rigor (thankfully, he is honest about this and points to areas where more rigor could be introduced, rather than giving the unnatural and awkward hybrid of rigor and intuition attempted by many calculus books). Second, a lot of the problems (though certainly not all) deal with pathological and/or special cases, so it's possible for teachers to give fairly onerous homeworks.

I bought this book to get a little more of the math than what was in Gleick's Chaos book from years ago. I haven't made it all the way through this book yet, but it's what I was looking for.