Understanding Nonlinear Dynamics [Paperback]

Daniel Kaplan (Author), Leon Glass (Author)

Book Description

ISBN-10: 0387944400 | ISBN-13: 978-0387944401 | Publication Date: April 13, 1995

This book presents the main concepts and applications of nonlinear dynamics at an elementary level. The book is based on a one-semester undergraduate course that has been given since 1975 at McGill University and has been constantly updated to keep up with current developments. Based on the authors' successful course for undergraduate students in the biological sciences, the primer presents the main concepts of non-linear dynamics at a level requiring only one year of calculus. This text will appeal to courses being offered in both mathematics and biology. Topics include finite difference equations, the concept of chaos, networks, cellular automata, on- and two-dimensional differential equations, the dynamics of non-linear equations, and linear stability analysis. Examples are all from the biological sciences, exercises are included in each chapter, and basic mathematical reviews are included in an appendix.

Editorial Reviews

Review

ANot only are many of the most recent topics included and simply explained, but the reader is also warned against difficulties in the practical implementation of the proposed methods of analysis and against common misinterpretations of some theoretical concepts. Because of its completeness and plain, but mathematically correct, style, this book is also an ideal starting point for researchers from various disciplines who are not familiar with mathematical concepts usually learned in the first two years of university study.A AMATHEMATICAL REVIEWS AI recommend this book strongly both to those who need to teach these topics and to those who want to learn about them, whether or not they are in the biosciences. In fact, I would strongly recommend this book to paleontologists, paleobiologists, paleoecologists, and geologists who are (finally) becoming interested in nonlinear dynamics, but are still afraid to ask.AAAMERICAN SCIENTIST A[The authors] have written a readily accessible introduction to nonlinear dynamicsAthe book presents the main concepts and applications of nonlinear dynamics at an elementary levelAInterspersed in the text are delightful short essays of a page or two eachACourses on nonlinear dynamics rarely present these topics at the level used in the bookAIt is written in a Auser friendlyA colloquial style and is a delight to readAno reader is likely to encounter a more accessible elementary introduction to nonlinear dynamics.AAPHYSICS TODAY

Product Details

• Paperback: 440 pages
• Publisher: Springer (April 13, 1995)
• Language: English
• ISBN-10: 0387944400
• ISBN-13: 978-0387944401
• Product Dimensions: 9.1 x 6.1 x 1 inches
• Shipping Weight: 1.4 pounds (View shipping rates and policies)
• Average Customer Review: 4.7 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #496,634 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

14 of 15 people found the following review helpful:

4.0 out of 5 stars A good introduction to the mechanical side..., May 30, 2002

By 

Yuri Kuzyk (Toronto, Ontario Canada) - See all my reviews

This review is from: Understanding Nonlinear Dynamics (Paperback)

It is funny that there is so much hype about Wolfram's "A New Kind of Science" when this book neatly pointed out his big 'discoveries' back in 1995. That is, all of Wolfram's opus can be found in chapter 2 of this book.

The book provides a good (and relatively gentle) introduction to the mechanistic view of non-linear dynamics. Many different applications of non-linear dynamics, from physics to biology, are overviewed and many detailed examples are provided. In all, this is a great reference.

The only shortcomings are the lack of discussions about frameworks, particularly mechanistic systems, and how they influence the applicability of the models. That is, some understanding of systems theory (von Bertalanffy in particular and the work of cybernetics as well) should have been included to point out the fact that the linear causality implied by many models immediately limits their applicability.

12 of 13 people found the following review helpful:

5.0 out of 5 stars Gentle introduction to nonlinear dynamics, July 23, 2001

By 

Steve Uhlig (Berlin, Germany) - See all my reviews
(REAL NAME)   

This review is from: Understanding Nonlinear Dynamics (Paperback)

This is a gentle introdution to nonlinear dynamics, maths are well explained, illustrations are abundant, the overview is very good overall, even if subjects are only touched. It could also serve as an introduction to finite-difference and differential equations for non-maths students.

Undergrads looking for something smooth on nonlinear dynamics should get this one...but for advanced readers it is probably a waste of time.

17 of 20 people found the following review helpful:

5.0 out of 5 stars Simply an Iluminating path to Understand Nonlinear Dynamics, February 12, 1998

By A Customer

This review is from: Understanding Nonlinear Dynamics (Texts in Applied Mathematics) (Hardcover)

It happens that in any field there is a book that iluminates. This is the one in Nonlinear Dynamics. With it's clear and simple but mathematically and conceptually rich presentation this text opens the mind towards the mathemathics that you learn in your two first University years, as aplicated to innumerable Life Science examples, but at the same time interesting for any other field's applications (Physics, Maths, Chemists,..). This book deals with Dynamics in a Superb Way. Contents: 1-Finite Difference Equations. 2-Boolean Networks and Celular Automata. 3-Self Similarity and Fractal Geometry. 4-One Dimensional Differential Equations. 5-Two Dimensional Differential Equations. 6-Time Series Analysis. Apendix-A: A Multifunctional Appendix. Appendix-B: A Note on Computer Notation. Buy it, you might learn how much you can do with you mathematics knowledge!