This book presents elements of the theory of chaos in dynamical systems in a framework of theoretical understanding coupled with numerical and graphical experimentation. The theory is developed using only elementary calculus and algebra, and includes dynamics of one-and two-dimensional maps, periodic orbits, stability and its quantification, chaotic behavior, and bifurcation theory of one-dimensional systems. There is an introduction to the theory of fractals, with an emphasis on the importance of scaling, and a concluding chapter on ordinary differential equations. The accompanying software, written in Java, is available online (see link below). The program enables students to carry out their own quantitative experiments on a variety of nonlinear systems, including the analysis of fixed points of compositions of maps, calculation of Fourier spectra and Lyapunov exponents, and box counting for two-dimensional maps. It also provides for visualizing orbits, final state and bifurcation diagrams, Fourier spectra and Lyapunov exponents, basins of attractions, three-dimensional orbits, Poincaré sections, and return maps.
Exploring Chaos: Theory And Experiment
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Book Description
Editorial Reviews
About the Author
Brian Davies is Reader in Mathematics at the Australian National University, with interests in mathematical physics, scientific computation, and the teaching of nonlinear dynamics and chaos. He has also held posts in Physics and Theoretical Physics, and in private and government research organizations. He has written the standard book on integral transforms, as well as numerous research articles in areas ranging from plasma physics and the design of turbines to phase transitions in magnetic systems.
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Most Helpful Customer Reviews
2 of 2 people found the following review helpful:
4.0 out of 5 stars
The practical approach,
This review is from: Exploring Chaos: Theory And Experiment (Studies in Nonlinearity) (Paperback)
I've had this book for some time and have used the associated software (downloaded from the internet) from time to time to illustrate some of the concepts to others. I would recommend the book for the software alone. It is an excellent work and a valuable addition to anyone's bookshelf.
The book contains a very practical introduction to nonlinear dynamics and the associated fractals. There is little theory here and one needs a good companion text if a deeper understanding of the theoretical foundations is required. The advantage of this approach is that the whole book can be read and understood with only a minimal mathematical background. (Lots of other books claim this but fall well short and require quite advanced knowledge of topology and set theory.) A star is lost for the usual reason: no worked solutions to the exercises.
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Inside This Book
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First Sentence:
To the Greeks, chaos signified the infinite formless space which existed before the universe was created. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
controlled logistic map, forward limit set, final state diagrams, prompt panel, superstable orbits, cobweb plot, tangent bifurcation, tent map, cobweb diagram, cubic map, using elementary algebra, intermittent behaviour, unimodal map, orbital density, first period doubling, interior crisis, coexisting attractors, capacity dimension, driven pendulum, exact orbits, area contraction, new fixed points, first return map, periodic orbits, critical parameter value New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
To the Greeks, chaos signified the infinite formless space which existed before the universe was created. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
controlled logistic map, forward limit set, final state diagrams, prompt panel, superstable orbits, cobweb plot, tangent bifurcation, tent map, cobweb diagram, cubic map, using elementary algebra, intermittent behaviour, unimodal map, orbital density, first period doubling, interior crisis, coexisting attractors, capacity dimension, driven pendulum, exact orbits, area contraction, new fixed points, first return map, periodic orbits, critical parameter value New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 19
books:
See all 19 books this book cites
2
books
cite this book:
- Dynamics: The Geometry of Behavior by Ralph Abraham in Front Matter, and Back Matter
- The Essence Of Chaos (The Jessie and John Danz Lecture Series) by Edward Lorenz on page 7, and Back Matter
- Classics On Fractals (Studies in Nonlinearity) by Gerald A. Edgar in Front Matter
- Introduction to Chaos and Coherence by J Froyland in Back Matter
- Deterministic Chaos: An Introduction by Heinz Georg Schuster in Back Matter
See all 19 books this book cites
- Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers by Robert Hilborn on page 42, and Back Matter
- Dynamics for Engineers by Soumitro Banerjee on page 273
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