Demonstrates how a basic knowledge of chaos theory can be used to evaluate chaotic experimental time series data and how to apply the presence of chaos to achieve practical goals. After familiarizing the reader with fundamental concepts of chaos, the text introduces the important topics of dimension, symbolic dynamics, Lyapunov exponents and entropy. Contains extensive reprints from major papers on the subject and concludes with a research bibliography of articles directed toward coping with chaos.
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From the Publisher
Demonstrates how a basic knowledge of chaos theory can be used to evaluate chaotic experimental time series data and how to apply the presence of chaos to achieve practical goals. After familiarizing the reader with fundamental concepts of chaos, the text introduces the important topics of dimension, symbolic dynamics, Lyapunov exponents and entropy. Contains extensive reprints from major papers on the subject and concludes with a research bibliography of articles directed toward coping with chaos.
From the Back Cover
The first unified presentation of new developments in the analysis and exploitation of chaotic systems... Mathematicians have been aware of chaotic dynamics since Poincar?'s work at the turn of the century. But, as the turn of yet another century approaches, physical scientists and engineers have begun to use their understanding of chaos theory to analyze chaotic experimental time series data. Some researchers have even used the presence of chaos to achieve practical goals. To do this, they have had to work with dynamical processes for which the equations were either not known or were too complex to be useful. In other words, they have been coping with chaos. Coping with Chaos is the first book to bring together recent advances in the interpretive and practical applications of chaos, which hold great promise for broad applicability throughout the physical sciences and engineering. Together with an introduction to chaos theory, this book provides detailed reports on methods of analyzing experimental time series data from chaotic systems and studies in which the unique attributes of chaos are put to practical use. Topics discussed in this book include:
* Theory of chaotic dynamics
* Embedding techniques for the analysis of experimental data
* Calculation of dimension and Lyapunov exponents
* Determination of periodic orbits and symbolic dynamics
* Prediction of chaotic time series
* Noise filtering of chaotic data
* Control of chaotic systems
* The use of chaotic signals for communication
* And more
* Theory of chaotic dynamics
* Embedding techniques for the analysis of experimental data
* Calculation of dimension and Lyapunov exponents
* Determination of periodic orbits and symbolic dynamics
* Prediction of chaotic time series
* Noise filtering of chaotic data
* Control of chaotic systems
* The use of chaotic signals for communication
* And more
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Inside This Book
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First Sentence:
The purpose of this chapter is to provide an elementary introduction to the subject of chaos. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
noisy orbit, double rotor map, modulated wavy vortex flow, uncontrolled chaotic attractor, two unstable foci, linear gaussian noise, local linear dynamics, true correlation dimension, spurious exponents, delay coordinate map, regulator poles, delay coordinate vector, aim equation, chaos using time delay, saddle orbits, generating surrogate data, experimental strange attractor, diode laser power, using delay coordinate embedding, system state point, quadratic predictors, filtered delay, flip saddle, trajectory matrix, thermal convection loop Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, College Park, University of Maryland, Department of Physics, Lecture Notes, University of California, San Diego, Los Alamos, Department of Energy, Fluid Mech, World Scientific, Elsevier Science Publishers, Nonlinear Oscillations, Edward Ott, National Science Foundation, Naval Surface Warfare Center, Office of Naval Research, Rev Lett, American Institute of Physics, Cambridge Univ, Celso Grebogi, Circuits Syst, Department of Electrical Engineering, Englewood Cliffs, Rajarshi Roy New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The purpose of this chapter is to provide an elementary introduction to the subject of chaos. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
noisy orbit, double rotor map, modulated wavy vortex flow, uncontrolled chaotic attractor, two unstable foci, linear gaussian noise, local linear dynamics, true correlation dimension, spurious exponents, delay coordinate map, regulator poles, delay coordinate vector, aim equation, chaos using time delay, saddle orbits, generating surrogate data, experimental strange attractor, diode laser power, using delay coordinate embedding, system state point, quadratic predictors, filtered delay, flip saddle, trajectory matrix, thermal convection loop Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, College Park, University of Maryland, Department of Physics, Lecture Notes, University of California, San Diego, Los Alamos, Department of Energy, Fluid Mech, World Scientific, Elsevier Science Publishers, Nonlinear Oscillations, Edward Ott, National Science Foundation, Naval Surface Warfare Center, Office of Naval Research, Rev Lett, American Institute of Physics, Cambridge Univ, Celso Grebogi, Circuits Syst, Department of Electrical Engineering, Englewood Cliffs, Rajarshi Roy 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 57
books:
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10
books
cite this book:
See all 10 books citing this book
- Dynamical Systems and Turbulence (Lecture Notes in Mathematics) by D. Rand on 8 pages
- Evolution, Learning and Cognition by Y. C. Lee on page 260, page 280, and Back Matter
- Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Applied Mathematical Sciences Vol. 42) by John Guckenheimer on page 91, and page 379
- Nonlinear Phenomena and Chaos (Malvern Physics Series) by S Sarkar on page 91, and page 116
- Iterated Maps on the Interval as Dynamical System by Pierre Collet on page 30, and page 190
See all 57 books this book cites
- Artificial War: Multiagent-Based Simulation of Combat by Andrew Ilachinski in Back Matter
- Fractal-Based Point Processes by Steven Bradley Lowen in Back Matter
- Mathematics for Mechanical Engineers by Frank Kreith on page 4
- Singular Spectrum Analysis: A New Tool in Time Series Analysis (Language of Science) by J.B. Elsner in Back Matter
- Perturbation Methods, Instability, Catastrophe and Chaos by C. F. Chan Man Fong in Back Matter
See all 10 books citing this book
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