Product Description

An introductory text in nonlinear dynamics and chaos, emphasizing applications in several areas of science, which include vibrations, biological rhythms, insect outbreaks, and genetic control systems. Contains a rich selection of illustrations, with many exercises and examples. Softcover.

Product Details

• Amazon Sales Rank: #35526 in Books
• Published on: 2001-01-18
• Original language: English
• Number of items: 1
• Binding: Paperback
• 512 pages

About the Author

Customer Reviews

Excellent introduction and reference text
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: 2/28/07

Now 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.

Template for a Math book!
Were all Math books written like this, the number of students majoring in Math, Physics, etc. would rise considerably. The presentation is clear, lucid and comprehensive. Each concept is introduced with its motivating phenomena and the mathematical treatment is logical and elegant with many worked examples. This is one of those rare Math books that "begin at the beginning", yet go on to develop the concepts to a point useful even to grad students who want a review of basics before plunging into more advanced material. (If you are looking for more detailed mathematical stuff, I'd suggest Kevorkian's "Multiple Scale and Singular Perturbation Methods" or "Perturbation Methods" by Hinch.)

For the benefit of those reviewers who have complained that the mathematics is not rigorous enough, may I point out that the author clearly states the book is an introduction to the topic. I have come across other introductory books using basic differential equations, on similar topics where the material is presented in a disjointed way. Strogatz, however, shows us the inter-relatedness of the broad range of concepts and applications that fall within the title. Therein lies a major strength of this book.

Another big plus is that Strogatz presents those intermediate diagrams and results that take us to the final conclusion. Also he interprets the Math en route to the finale. He does not employ the usual "it is apparent that ..." strategy to pole-vault to miracle steps. This approach makes the book a breezy read; a remark not commonly made about advanced Math books!

Great intro to nonlinear dynamics with excellent examples
This book is an excellent introductory graduate level text on nonlinear dynamics for those who wish to understand the basic concepts before seeing the mathematical rigor at the heart of the subject. Strogatz avoids getting caught up in mathematical nuances which often cloud the big picture for non-math students, and thereby clearly impresses upon the reader the essence of nonlinear dynamics, eventually building up to chaos. The examples and problems are truly unique and inspiring. This book is an excellent starting place for someone who knows little or nothing about nonlinear dynamics but has done some basic work with linear differential equations and linear algebra.