Discrete Chaos, Second Edition: With Applications in Science and Engineering [Hardcover]

Saber N. Elaydi (Author)

Book Description

ISBN-10: 1584885920 | ISBN-13: 978-1584885924 | Publication Date: November 9, 2007 | Edition: 2

While maintaining the lucidity of the first edition, Discrete Chaos, Second Edition: With Applications in Science and Engineering now includes many recent results on global stability, bifurcation, chaos, and fractals. The first five chapters provide the most comprehensive material on discrete dynamical systems, including trace-determinant stability, bifurcation analysis, and the detailed analysis of the center manifold theory. This edition also covers L-systems and the periodic structure of the bulbs in the Mandelbrot set as well as new applications in biology, chemistry, and physics. The principal improvements to this book are the additions of PHASER software on an accompanying CD-ROM and the Maple™ and Mathematica^® code available for download online.

Incorporating numerous new topics and technology not found in similar texts, Discrete Chaos, Second Edition presents a thorough, up-to-date treatment of the theory and applications of discrete dynamical systems.

Editorial Reviews

Review

From the Foreword:
The present text book gives an excellent introduction to this new, and potentially revolutionary, territory. It will take the reader, with clarity and precision, from simple beginnings with 1-dimensional difference equations (and their cascades of period doubling en route to chaos), on to 2- and 3-dimensional systems, and beyond this to fractals and relationships between geometry and dynamics. The final chapter deals with the Julia and Mandelbrot sets, where in my opinion mathematical elegance and pure aesthetic beauty begin to merge.
-Lord Robert M. May, Department of Zoology, University of Oxford, UK

One of the features that makes this book unique is that, as a renowned and active researcher in discrete dynamical systems and difference equations, Elaydi integrates very skillfully these two fields, whenever possible, and provides in depth the stability theory for one- and two-dimensional dynamical systems. It is fascinating that, without sacrificing anything important, the author is able to simplify the treatment and compress the material on one-dimensional dynamics into chapter 1 that takes some texts many chapters.
-Danrun Huang, St. Cloud State University, Minnesota, USA

About the Author

Trinity University, San Antonio, Texas, USA --This text refers to an out of print or unavailable edition of this title.

Product Details

• Hardcover: 440 pages
• Publisher: Chapman and Hall/CRC; 2 edition (November 9, 2007)
• Language: English
• ISBN-10: 1584885920
• ISBN-13: 978-1584885924
• Product Dimensions: 9.4 x 6.4 x 1.1 inches
• Shipping Weight: 1.5 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #952,233 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

11 of 11 people found the following review helpful:

5.0 out of 5 stars A notable entry with a new perspective, February 10, 2000

By 

Hassan Sedaghat - See all my reviews

This review is from: Discrete Chaos, Second Edition: With Applications in Science and Engineering (Hardcover)

"Discrete Chaos" resembles in many ways the highly successful 1989 introductory text by Robert Devaney on chaotic dyanamical systems. However, a great deal has happened since Devaney's text appeared, and Discrete Chaos includes some of the new finds (e.g., the new results on stability of maps on the real line and the author's own work on the converse of Sharkovsky's Theorem). Discrete Chaos also adds a new element unique to it: The author's perspective as a successful researcher and a talented expositor in the area of difference equations. This is important since it balances the attention between the familiar topological/algebraic ideas and the more purely analytical results. Equally important perhaps, is the author's talent for writing introductory level books (he also wrote the very readable "An Introduction to Difference Equations"). Discrete Chaos contains many interesting examples and helpful exercises, although the proofs of the more technical results are not given.

9 of 9 people found the following review helpful:

5.0 out of 5 stars Accessible Chaos Theory, March 7, 2000

By 

Abdul-Aziz Yakubu (USA) - See all my reviews

This review is from: Discrete Chaos, Second Edition: With Applications in Science and Engineering (Hardcover)

Discrete chaos is an excellent text. It can serve both as an introductory text in discrete-time dynamical systems (chaos theory) and as a resource for more advanced work. The book provides an accessible introduction to discrete-time dynamical systems with many interesting applications.

The book is divided into six sections. Section 1 and Section 2 introduce essential concepts for describing and analyzing chaotic discrete-time systems. Section 3 and Section 5 focus on chaos in one dimension and two dimensions, respectively. Section 4 describes the stability of two-dimensional systems. Fractals are formulated and analyzed in Section 6. Section 7 is devoted to the study of The Julia and Mandelbrot Sets.

All chapters end with excellent exercises. The book also has answers to the exercises. The book is designed to be independent of any particular computing environment.

8 of 8 people found the following review helpful:

5.0 out of 5 stars Truely Exceptional: Order within chaos, April 19, 2000

By A Customer

This review is from: Discrete Chaos, Second Edition: With Applications in Science and Engineering (Hardcover)

This book is highly recommended to all those who aspire to enjoy the world of chaos and fractals. It is written by one of the masters of discrete dynamics and difference equations. I was sold on Devaney's book until I saw this book. Moreover, I am not fully satisfied with the explanations and the writing style in the book by Alligood, Sauer and Yorke. At last we have some genuine and realistic applications to discrete dynamical systems. The best bargain of all is the chapter on Iterated function systems; the book provides a delightful and very readable , yet mathematically honest, account. Almost all the results in the book are proved completely and clearly. I enjoyed the relaxed and lucid writing style of this author. Keep them coming and way to go Elaydi!