Understanding Nonlinear Dynamics

Book Description

UNDERSTANDING NONLINEAR DYNAMICS is based on an undergraduate course taught for many years to students in the biological sciences. The text provides a clear and accessible development of many concepts from contemporary dynamics, including stability and multistability, cellular automata and excitable media, fractals, cycles, and chaos. A chapter on time-series analysis builds on this foundation to provide an introduction to techniques for extracting information about dynamics from data. The text will be useful for courses offered in the life sciences or other applied science programs, or as a supplement to emphasize the application of subjects presented in mathematics or physics courses. Extensive examples are derived from the experimental literature, and numerous exercise sets can be used in teaching basic mathematical concepts and their applications. Concrete applications of the mathematics are illustrated in such areas as biochemistry, neurophysiology, cardiology, and ecology. The text also provides an entry point for researchers not familiar with mathematics but interested in applications of nonlinear dynamics to the life sciences.

Customer Reviews:

A good introduction to the mechanical side..........2002-05-30

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.

Gentle introduction to nonlinear dynamics.......2001-07-24

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.

Simply an Iluminating path to Understand Nonlinear Dynamics.......1998-02-13

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!

Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics (Applied Mathematical Sciences)

Average customer rating:

Excellent Book!

Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics (Applied Mathematical Sciences)
Andrzej Lasota , and Michael C. Mackey
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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Options, Futures and Other Derivatives (6th Edition)

ASIN: 0387940499

Book Description

This book gives a unified treatment of a variety of mathematical systems generating densities, ranging from one-dimensional discrete time transformations through continuous time systems described by integro-partial-differential equations. Examples have been drawn from a variety of the sciences to illustrate the utility of the techniques presented. This material was organized and written to be accessible to scientists with knowledge of advanced calculus and differential equations. In various concepts from measure theory, ergodic theory, the geometry of manifolds, partial differential equations, probability theory and Markov processes, and chastic integrals and differential equations are introduced. The past few years have witnessed an explosive growth in interest in physical, biological, and economic systems that could be profitably studied using densities. Due to the general inaccessibility of the mathematical literature to the non-mathematician, there has been little diffusion of the concepts and techniques from ergodic theory into the study of these "chaotic" systems. This book intends to bridge that gap.

Customer Reviews:

Excellent Book!.......2000-12-20

This is one of my favorite maths books. My interest in it is not so much for the discussion of chaotic systems, but more for that on stochastically perturbed systems. As far as this topic goes, this is the best book I've found in the field by far. The treatment is careful and self-contained, and the proofs are clear throughout. Lots of intuition is given with each result.

Book Description

This book develops deterministic chaos and fractals from the standpoint of iterated maps, but the method of analysis and choice of emphasis make it very different from all other books in the field. It is written to provide the reader with an introduction to more recent developments, such as weak universality, multifractals, and shadowing, as well as to older subjects such as universal critical exponents, devil's staircases, and the Farey tree. Throughout the book the author uses a fully discrete method, a "theoretical computer arithmetic," because finite (but not fixed) precision is a fact of life that cannot be avoided in computation or in experiment. This approach leads to a more general formulation in terms of symbolic dynamics and to the idea of weak universality. The author explains why continuum analysis, computer simulations, and experiments form three entirely distinct approaches to chaos theory. In the end, the connection is made with Turing's ideas of computable numbers. It is explained why the continuum approach leads to predictions that are not necessarily realized in computations or in nature, whereas the discrete approach yields all possible histograms that can be observed or computed.

Customer Reviews:

WoW.......2007-07-18

I think Prof. McCauley is the smartest man on the face of the earth. He must have wonderful, beautiful, smart children.

Regular and Chaotic Dynamics (Applied Mathematical Sciences)

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Regular and Chaotic Dynamics (Applied Mathematical Sciences)
A.J. Lichtenberg , and M.A. Lieberman
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0387977457

Book Description

This book treats nonlinear dynamics in both Hamiltonian and dissipative systems. The emphasis is on the mechanics for generating chaotic motion, methods of calculating the transitions from regular to chaotic motion, and the dynamical and statistical properties of the dynamics when it is chaotic. The book is intended as a self consistent treatment of the subject at the graduate level and as a reference for scientists already working in the field. It emphasizes both methods of calculation and results. It is accessible to physicists and engineers without training in modern mathematics. The new edition brings the subject matter in a rapidly expanding field up to date, and has greatly expanded the treatment of dissipative dynamics to include most important subjects. It can be used as a graduate text for a two semester course covering both Hamiltonian and dissipative dynamics.

Hamiltonian Chaos and Fractional Dynamics

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Hamiltonian Chaos and Fractional Dynamics
George M. Zaslavsky
Manufacturer: Oxford University Press, USA
ProductGroup: Book
Binding: Hardcover

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ASIN: 0198526040

Book Description

The dynamics of realistic Hamiltonian systems has unusual microscopic features that are direct consequences of its fractional space-time structure and its phase space topology. The book deals with the fractality of the chaotic dynamics and kinetics, and also includes material on non-ergodic and non-well-mixing Hamiltonian dynamics. The book does not follow the traditional scheme of most of today's literature on chaos. The intention of the author has been to put together some of the most complex and yet open problems on the general theory of chaotic systems. The importance of the discussed issues and an understanding of their origin should inspire students and researchers to touch upon some of the deepest aspects of nonlinear dynamics. The book considers the basic principles of the Hamiltonian theory of chaos and some applications including for example, the cooling of particles and signals, control and erasing of chaos, polynomial complexity, Maxwell's Demon, and others. It presents a new and realistic image of the origin of dynamical chaos and randomness. An understanding of the origin of randomness in dynamical systems, which cannot be of the same origin as chaos, provides new insights in the diverse fields of physics, biology, chemistry, and engineering.

Images of a Complex World: The Art and Poetry of Chaos

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Truth and Beauty

Images of a Complex World: The Art and Poetry of Chaos
Robin S. Chapman , and Julien Clinton Sprott
Manufacturer: World Scientific Publishing Company
ProductGroup: Book
Binding: Paperback

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ASIN: 9812564012

Product Description

This coffee-table book will delight and inform general readers curious about ideas of chaos, fractals, and nonlinear complex systems. Developed out of ten years of interdisciplinary seminars in chaos and complex systems at the University of Wisconsin-Madison, it features multiple ways of knowing: Robin Chapmans poems of everyday experience of change in a complex world, associated metaphorically with Julien Clinton Sprotts full-color computer art generated from billions of versions of only three simple equations for strange attractors, Julia sets, and iterated function systems; his definitions of 39 key terms; a mathematical appendix; and even a multiple-choice quiz to test understanding. Accompanied by a CD-ROM of the poet reading 13 poems and 1,000 images of chaos art from which slide shows can be generated and 100 high-resolution posters created. With a foreword by Cliff Pickover, author of A Passion for Mathematics.

Customer Reviews:

Truth and Beauty.......2005-11-16

I had the good fortune to see this book in the making when it was a thick sheaf of flimsy printer paper. The words and images collided in gorgeous ways, and I knew something special was taking form.

I love what Robin Chapman and Clint Sprott have done. I love this book. More collaborations like this should be undertaken. It deepens our sensibilities. It enlarges our world. It does something graceful for the heart. The fractal images are beautifully rendered and Sprott's clear, concise definitions of key terms illuminate them for the lay reader. Chapman's poems are in perfect alignment with both the fractals and definitions, showing us "life on the edge of change at every scale."

Here's a coffee table book that goes beyond decoration. Here's a book of poetry that goes beyond words. Here's science that makes itself accessible. I highly recommend this book to artists, scientists, and everyone else who wants to make the connections that help us explain our world and our lives.

Chaotic Vibrations: An Introduction for Applied Scientists and Engineers

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Chaotic Vibrations: An Introduction for Applied Scientists and Engineers
Francis C. Moon
Manufacturer: Wiley-Interscience
ProductGroup: Book
Binding: Hardcover

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ASIN: 0471856851

Book Description

Translates new mathematical ideas in nonlinear dynamics and chaos into a language that engineers and scientists can understand, and gives specific examples and applications of chaotic dynamics in the physical world. Also describes how to perform both computer and physical experiments in chaotic dynamics. Topics cover Poincare maps, fractal dimensions and Lyapunov exponents, illustrating their use in specific physical examples. Includes an extensive guide to the literature, especially that relating to more mathematically oriented works; a glossary of chaotic dynamics terms; a list of computer experiments; and details for a demonstration experiment on chaotic vibrations.

Chaos, Fractals, and Dynamics (Lecture Notes in Pure and Applied Mathematics)

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Chaos, Fractals, and Dynamics (Lecture Notes in Pure and Applied Mathematics)
Fischer
Manufacturer: CRC
ProductGroup: Book
Binding: Paperback

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Chaotic and Fractal Dynamics: An Introduction for Applied Scientists and Engineers

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Fractal, Chaos, IFS

Chaotic and Fractal Dynamics: An Introduction for Applied Scientists and Engineers
Francis C. Moon
Manufacturer: Wiley-Interscience
ProductGroup: Book
Binding: Hardcover

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ASIN: 0471545716

Book Description

A revision of a professional text on the phenomena of chaotic vibrations in fluids and solids. Major changes reflect the latest developments in this fast-moving topic, the introduction of problems to every chapter, additional mathematics and applications, more coverage of fractals, numerous computer and physical experiments. Contains eight pages of 4-color pictures.

Customer Reviews:

Fractal, Chaos, IFS.......2000-05-10

I want some more information about the book

Chaos, Fractals, and Dynamics - Computer Experiments in Mathematics

Average customer rating:

helpful, easy to understand, straightforward
Nice introduction to Chaos and Fractals!

Chaos, Fractals, and Dynamics - Computer Experiments in Mathematics
Robert L. Devaney
Manufacturer: Addison-Wesley Publishing
ProductGroup: Book
Binding: Paperback

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The Essence of Chaos (The Jessie and John Danz Lecture Series)

ASIN: 020123288X

Customer Reviews:

helpful, easy to understand, straightforward.......1999-01-04

This book provides an excellent framework for understanding chaotic systems, whether for the novice or the experienced fractal scientist. The diagrams in particular helped elucidate the concepts presented. Science made simple without being dummed down - well done!

Nice introduction to Chaos and Fractals!.......1996-05-23

This is a nice little book whose target audience is high school students, beginning undergraduates, and science teachers. Using many examples , Devaney leads the reader through ideas of iteration and dynamical system. The latter half of the book deals with the connection between chaos and the science of fractals. The readers are encouraged to explore the various facets of chaos and fractals using simple computer programs (many sample source codes are peppered throughout the book). In addition to the book, there is a couple of companion video tapes that are also highly instructive and serve as good introduction to chaos and fractals. The first video, Chaos, Fractals and Dynamics, bears the same name as the book and brings to life many of the examples mentioned in the book in a manner that is not possible via the static book format. The visual highlight occurs when Devaney shows beautiful animations of the Julia set. If this doesn't get the students excited, I don't know what will! The second video, Transition to Chaos, describes the period-doubling approach to chaos using the now standard quadratic map. There is a nice discussion about the relationship between the period-doubling bifurcation and the Mandelbrot and Julia sets.

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Rumi's Wisdom

The Hundred Tales of Wisdom: Life, Teachings and Miracles of Jalaludin Rumi from Aflaki's Munaqib
Jalaludin Rumi , and Shamsuddin Ahmad Aflaki
Manufacturer: Octagon Press, Limited
ProductGroup: Book
Binding: Paperback

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The Exploits of the Incomparable Mulla Nasrudin / The Subtleties of the Inimitable Mulla Nasrudin

ASIN: 0863040497

Book Description

Christians and Jews, as well as Muslims, called Jalaludin Rumi their teacher. Born in Afghanistan in the 13th century, Rumi is widely considered one of the greatest mystical teachers, and perhaps the greatest mystical poet of all time.

An important theme of Rumi's work is the danger of mistaking the "container for the content." He regarded even his own poetry as a "container" for the real purpose of his work.

"The Hundred Tales of Wisdom" is a collection of events and "action teachings" from Rumi's life, with stories, fables and verse from his work. This classic is part of the series of basic writings now being issued by Octagon Press.

Customer Reviews:

Rumi's Wisdom.......2000-02-01

This Middle Eastern classic by the great Sufi mystic & poet Jalaludin Rumi has been a part of Sufi study for 700 years. Part biography and part anthology, its tales, anecdotes and narratives are still used to develop insights beyond ordinary perceptions. Rumi taught Christians, Jews and Muslims alike. This may account for his current appeal. He is much in vogue in the West. His major work, The Mathnavi-i-Maanavi (Couplets of Inner Meaning) is considered to be one of the world's greatest books.

"You get out of it what is in it for you." wrote Rumi. He also wrote, "Do not look at my outward shape, but take what is in my hand."

The Hundred Tales of Wisdom is full of surprising; often shocking tales. Some are very funny. I think it may be better appreciated and better understood by those familiar with Idries Shah's The Sufis, Commanding Self and Knowing how to Know.

I think this book will appeal to those interested in Rumi's life and work or in Eastern thought and classical literature. It may also appeal to lovers of inspirational literature.... and to those who search for a clear understanding of themselves and their possibilities.

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