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Chaos and Dynamical Systems
Chaos and Dynamical Systems presents an accessible, clear introduction to dynamical systems and chaos theory, important and exciting areas that have shaped many scientific fields. While the rules governing dynamical systems are well-specified and simple, the behavior of many dynamical systems is remarkably complex. Of particular note, simple deterministic dynamical systems produce output that appears random and for which long-term prediction is impossible. Using little math beyond basic algebra, David Feldman gives readers a grounded, concrete, and concise overview.
In initial chapters, Feldman introduces iterated functions and differential equations. He then surveys the key concepts and results to emerge from dynamical systems: chaos and the butterfly effect, deterministic randomness, bifurcations, universality, phase space, and strange attractors. Throughout, Feldman examines possible scientific implications of these phenomena for the study of complex systems, highlighting the relationships between simplicity and complexity, order and disorder.
Filling the gap between popular accounts of dynamical systems and chaos and textbooks aimed at physicists and mathematicians, Chaos and Dynamical Systems will be highly useful not only to students at the undergraduate and advanced levels, but also to researchers in the natural, social, and biological sciences.
In initial chapters, Feldman introduces iterated functions and differential equations. He then surveys the key concepts and results to emerge from dynamical systems: chaos and the butterfly effect, deterministic randomness, bifurcations, universality, phase space, and strange attractors. Throughout, Feldman examines possible scientific implications of these phenomena for the study of complex systems, highlighting the relationships between simplicity and complexity, order and disorder.
Filling the gap between popular accounts of dynamical systems and chaos and textbooks aimed at physicists and mathematicians, Chaos and Dynamical Systems will be highly useful not only to students at the undergraduate and advanced levels, but also to researchers in the natural, social, and biological sciences.
262 pages, Paperback
Published August 6, 2019
5 people are currently reading
125 people want to read
About the author
David P. Feldman
3 books7 followersDavid Feldman is Professor of Physics and Mathematics at College of the Atlantic. He is the author of two books: Chaos and Fractals: An Elementary Introduction (Oxford University Press, 2012), a textbook for non-math/science majors; and Chaos and Dynamical Systems (Princeton University Press, 2019), a contribution to the Primers in Complex Systems series. Dave has developed two MOOCs, one on Chaos and Dynamical Systems and one on Fractals and Scaling. These free, online classes are part of the Santa Fe Institute's Complexity Explorer project and have been taken by thousands of students. He is currently working on a textbook on renewable energy.
Dave has taught over twenty different classes in physics, math, and computer science at College of the Atlantic. He served as COA's Associate Dean for Academic Affairs from 2003-07. Dave served as Co-director of the Santa Fe Institute's Complex Systems Summer School (CSSS) in Beijing, China from 2006-08 and since 2017 has directed the Santa Fe CSSS. From December 2018 to August 2019 he was the Interim Vice-President for Education at the Santa Fe Institute. Dave was a U.S. Fulbright lecturer in Rwanda in 2011-12.
Dave is a theoretical and computational physicist whose research interests lie in the fields of statistical mechanics and nonlinear dynamics. He is the author of "Chaos and Fractals: An Elementary Introduction," Oxford University Press (2012), a textbook for non-science majors. This book is based on a course he has taught at College of the Atlantic for over a decade.
Dave has taught over twenty different classes in physics, math, and computer science at College of the Atlantic. He served as COA's Associate Dean for Academic Affairs from 2003-07. Dave served as Co-director of the Santa Fe Institute's Complex Systems Summer School (CSSS) in Beijing, China from 2006-08 and since 2017 has directed the Santa Fe CSSS. From December 2018 to August 2019 he was the Interim Vice-President for Education at the Santa Fe Institute. Dave was a U.S. Fulbright lecturer in Rwanda in 2011-12.
Dave is a theoretical and computational physicist whose research interests lie in the fields of statistical mechanics and nonlinear dynamics. He is the author of "Chaos and Fractals: An Elementary Introduction," Oxford University Press (2012), a textbook for non-science majors. This book is based on a course he has taught at College of the Atlantic for over a decade.
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Displaying 1 - 3 of 3 reviews
February 27, 2021
I highly recommend reading this book to anyone interested in chaos theory and complex systems. Being only the tip of an iceberg, the book introduces main mathematical bases of the chaos and dynamical systems via oversimplified examples and illustrations without being overwhelmingly mathematical. The book is comprehensible for anyone with only basic knowledge of differential equations and the author's deep understanding of the issue enables the readers to enjoy understanding the otherwise inaccessible mathematical concepts.
December 12, 2023
Riveting!
I read this during my differential calculus class and learned more from the book than I would have from the class.
I read this during my differential calculus class and learned more from the book than I would have from the class.
January 7, 2022
While reading this book I slowly began to realize that my very existence could be determined by a system of rather simple differential equations. How am I to prove otherwise? Any observer would tell me that my life appears to be random but I would remind them that an algorithmically random series is actually predictable to a certain degree given a precise enough initial condition. I began to wonder which would be worse, a universe in which everything has already been predetermined or one in which everything is entirely stochastic? A relinquishment of control over my own life appealed to me. I wouldn't really be deciding anything but at least I could feel like I was.
As I continued to read on however, I realized that I do in fact possess free will--just not in the broad sense that most of us like to believe. I was introduced to the concept of a strange attractor, a generalized pattern that a dynamical system tends towards and eventually evolves into over enough time no matter what initial condition is given. Within this attractor, the system is able to behave chaotically on a local level; its moment to moment behavior is aperiodic. However, if you were to zoom out and view the bigger picture, you would see that the system is following a predictable track. This leads to a revelation--globally stable systems can emerge from localized chaotic ones. Enter my own existence...
I also really enjoyed the section on bifurcations. This concept came very intuitively to me. The discovery of universality within bifurcations, however, was mind blowing. This is one of my favorite non-fiction reads. Check it out if you want your perception of reality shattered.
As I continued to read on however, I realized that I do in fact possess free will--just not in the broad sense that most of us like to believe. I was introduced to the concept of a strange attractor, a generalized pattern that a dynamical system tends towards and eventually evolves into over enough time no matter what initial condition is given. Within this attractor, the system is able to behave chaotically on a local level; its moment to moment behavior is aperiodic. However, if you were to zoom out and view the bigger picture, you would see that the system is following a predictable track. This leads to a revelation--globally stable systems can emerge from localized chaotic ones. Enter my own existence...
I also really enjoyed the section on bifurcations. This concept came very intuitively to me. The discovery of universality within bifurcations, however, was mind blowing. This is one of my favorite non-fiction reads. Check it out if you want your perception of reality shattered.
Displaying 1 - 3 of 3 reviews