Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering (Studies in Nonlinearity) 1st Edition

by Steven H. Strogatz (Author)

72 customer reviews

ISBN-13: 978-0738204536

ISBN-10: 0738204536

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Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (Studies in Nonlinearity)
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This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.A unique feature of the book is its emphasis on applications. These include mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with the mathematical theory.Richly illustrated, and with many exercises and worked examples, this book is ideal for an introductory course at the junior/senior or first-year graduate level. It is also ideal for the scientist who has not had formal instruction in nonlinear dynamics, but who now desires to begin informal study. The prerequisites are multivariable calculus and introductory physics.

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Product Details

Series: Studies in Nonlinearity
Paperback: 512 pages
Publisher: Westview Press; 1 edition (January 19, 2001)
Language: English
ISBN-10: 0738204536
ISBN-13: 978-0738204536
Product Dimensions: 6.1 x 1.2 x 9.2 inches
Shipping Weight: 1.6 pounds
Average Customer Review: 4.8 out of 5 stars See all reviews (72 customer reviews)
Amazon Best Sellers Rank: #220,698 in Books (See Top 100 in Books)
- #6 in Books > Science & Math > Mathematics > Applied > Biomathematics
- #28 in Books > Science & Math > Physics > Chaos Theory
- #104 in Books > Science & Math > Reference

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Customer Reviews

4.8 out of 5 stars

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Most Helpful Customer Reviews

118 of 120 people found the following review helpful

Excellent introduction and reference text

By Reviewer on March 7, 2003

Format: Paperback Verified Purchase

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.

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76 of 76 people found the following review helpful

Template for a Math book!

By A reader on March 28, 2005

Format: Paperback

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!

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33 of 34 people found the following review helpful

Great intro to nonlinear dynamics with excellent examples

By A Customer on July 27, 1998

Format: Hardcover

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.

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28 of 29 people found the following review helpful

Nice intuitive introduction to chaos and nonlinear phenomena

By Josh Isralowitz on November 24, 2003

Format: Paperback

Basically, if you have a solid foundation in elementary multivariable calculus (calc III) and some aspects of ODEs, and want to know just what's going on with this new 'chaos trend,' and more importantly want to know why 'chaos' is actually useful, then read this book. As one reviewer noted, this book is not mathematically rigorous, and there's a simple reason for this: one can't explain nonlinear phenomena rigorously with just an elementary multivariable calculus backround. To rigorously treat the material in this book, you must have at least some point-set topological backround and have a decently strong real analysis backround (even Strogatz uses concepts from analysis and topology in an elementary way, such as compactness and measure) and even more advanced books that assume such a backround are sometimes less than rigorous (i.e. 'Perko' often says 'it can be shown' rather than showing it himself.) However, the lack of rigor I think is a good thing. Strogatz always nicely indicates 'why something should be true,' which for a beginner will give them a intuition about the subject so that if they gain the backround mentioned above, they can dive farther into this subject by using other advanced books. Finally, this book should be used as a third year undergraduate text. It should not be used as an advanced undergraduate/first year graduate text, since such courses should be more in depth and rigorous.

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Most Recent Customer Reviews

Far reaching consequences.

Steve is a smart guy.

Published 2 months ago by Fred Concklin

The book teaches how to approach problems and which techniques work...

An outstanding textbook that avoids the usual mathematics pitfall of being painfully dry. The book teaches how to approach problems and which techniques work best for which... Read more

Published 2 months ago by User

Simply the best!

No review can properly describe the value of this book. Simply the best!

Published 2 months ago by mike kovy

Great intro to Nonlinear Dynamics

Initially, I strongly disliked this book and the course I was taking it along side of. However, I found that Strogatz has his lectures on Youtube for this course and I started... Read more

Published 3 months ago by William F. Blake

Five Stars

Published 4 months ago by lambrechts

5 stars

Great introductory undergraduate book for dynamics.

Published 10 months ago by Differential Manifold

... both beginners and experts that want to keep a good reference.

It's the right book for both beginners and experts that want to keep a good reference.

Published 11 months ago by fpnc

Beginners guide to practical nonlinear dynamics

A wonderful book with very realsitic examples and a clear presentation of the main ideas of nonlinear dynamics. A must have for your collection

Published 11 months ago by Rajesh R Parwani

A fantastic book. The narrative is a bit informal

A fantastic book. The narrative is a bit informal, which makes the subject slight. The analysis is performed using a simple mathematical basis, at the undergraduate level. Read more

Published 11 months ago by William Schroeder Cardozo

Five Stars

A good advanced math book, and into to chaos.

Published 12 months ago by C George Brockus