Table Of ContentEXPLORING
CHAOS
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Library of Congress Cataloging-in-Publication Data
ISBN 13: 978-0-8133-4127-9 (pbk)
STUDIES IN NONLINEARITY
Robert L. Devaney, Boston University, Editor
Chaotic dynamics has been hailed as the third great scientific revolution of the twenti
eth century, along with relativity and quantum mechanics. The explosion of interest in
nonlinear systems has led to the development of the Advanced Book Program's Studies
in Nonlinearity series. This unique, interdisciplinary publishing program makes excit
ing new developments in nonlinear studies available to the scientific community.
Studies in Nonlinearity's textbooks, monographs, and reference books are targeted for
advanced undergraduate and beginning graduate students, as well as researchers. The
series aims to make new mathematical developments in this area accessible to a wide
audience, including mathematicians, physicists, chemists, engineers, computer scien
tists, biologists, and economists.
Dynamics of Complex Systems
Yaneer Bar-Yam
Nonlinear Dynamics and Chaos
Steven Strogatz
Classics on Fractals
Gerald A. Edgar
A First Course in Chaotic Dynamical Systems
Theory and Experiment
Robert L. Devaney
Dynamical Systems Software
A First Course in Chaotic Dynamical Systems Software Labs: 1-6
James Georges and Del Johnson
An Experimental approach to Nonlinear Dynamics and Chaos
With Macintosh disk
Nicholas B. Tufillaro, Tyler Abbott, and Jeremiah Reilly
An Eye for Fractals
Michael McGuire
Chaos, Fractals, and Dynamics
Computer Experiments in Mathematics
Robert L. Devaney
An Introduction to Chaotic Dynamical Systems
Second Edition
Robert L. Devaney
Exploring Chaos
Theory and Experiment
Brian Davies
to Patricia
Preface
An introduction to non-linear dynamics and chaos is important to many
of today's students, not just in the physical sciences, but in a multitude of
disciplines where dynamical processes play a vital role. The same students,
however, are under great pressure to fit numerous other subjects into their
university curriculum. Such pressures, operating since secondary college,
have already set a pattern: students whose interest is high, whose time is
limited, and whose mathematical training is modest. The popularisation of
chaos is partly responsible for the interest, it is also responsible for many
misunderstandings which need to be dispelled.
This project has evolved from several years of teaching such students. I
have tried to develop material which offers opportunity to observe typical
non-linear behaviour, and to afford adequate theoretical explanation of key
features, using only a minimum of advanced mathematics. For the most
part, this means elementary algebra and calculus. As the project unfolded,
I became increasingly convinced that students must be enabled to make
their own numerical experiments, but that most have neither the time nor
the expertise to write their own programs. The present offering, therefore,
is more than just a text; I have integrated the theory with software which
has been developed in parallel. The intention is that, in as many places
as possible, there should be a simple mathematical explanation and ap
propriate computational tools for each important concept, together with
visualisation in a modern graphical environment.
The choice of topics, and the order of their presentation, reflects the
tension between the desire to cover the most important parts of the subject
and the need to keep the material at an elementary level. Another crite
rion was that I did not wish too often to go beyond what a reader could
reasonably check for him/herself without further theoretical preparation.
As well as these considerations, it is hardly necessary to compete with the
many excellent advanced books already in print, equally it is not my aim
to overlap with other noteworthy books which expound the subject with
virtually no mathematics at all. Some of these books, in both categories,
are listed in the bibliography; it goes without saying that I owe a debt to
each and every one. Because this is an introductory work the bibliography
does not contain references to original articles, however a few are scattered
throughout the footnotes where it seemed appropriate.
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