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Chaos : From Theory to Applications :  From Theory to Applications - Anastasios A. Tsonis

Chaos : From Theory to Applications

From Theory to Applications


Published: 1992
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While many books have been written on chaos, this unique work bridges the gap between theory and application to help both scientists and students use the theory of nonlinear dynamical systems in their own field of research. Including numerous examples, the volume will serve as a text for an upper-level undergraduate or graduate course, as well as a reference source for the researcher.

Introductionp. 3
Mathematical Notesp. 7
Probability Distributions Expectations, and Momentsp. 7
The Autocorrelation and Spectral Density Functionsp. 8
Stability Analysisp. 17
Physics Notesp. 33
Conservative versus Dissipative Dynamical Systemsp. 33
Integrable and Nonintegrable Dynamical Systemsp. 42
Ergodic versus Nonergodic Dynamic Systemsp. 44
Autonomous Systemsp. 45
On Fractalsp. 49
Topological, Euclidean, and Fractal Dimensionsp. 49
A General Way to Measure the Fractal Dimensionp. 52
Some Interesting Properties of Fractal Objectsp. 53
'Fractality' in Time Seriesp. 55
Power Spectra for Fractional Brownian Motions and the Exponent Hp. 60
Attractorsp. 67
Strange Attractorsp. 73
Some Other Examples of Dissipative Systems Exhibiting Strange Attractorsp. 78
Delineating and Quantifying the Dynamicsp. 83
Determining the Various Dimensions and Lyapunov Exponents for a System of Ordinary Differential Equationsp. 94
Multiple Attractors and Fractal Basinsp. 97
An Obvious Questionp. 100
Bifurcations and Routes to Chaosp. 103
Hopf Bifurcationp. 103
Pitchfork Bifurcation and Period Doublingp. 107
Flip Bifurcation and Period Doublingp. 115
Explosive Bifurcationsp. 118
Fold Bifurcationp. 119
Universality and Routes to Chaosp. 126
The Genesis of a Strange Attractorp. 131
Chaos: A Synonym of Randomness and Beautyp. 132
Chaos Elsewherep. 137
Hamiltonian Chaosp. 137
Quantum Chaosp. 141
Low-Dimensional Chaos in Infinite-Dimensional Systemsp. 142
Reconstruction of Dynamics from Observablesp. 149
Phase-Space Reconstruction - Method of Delaysp. 149
The Choice of [tau]p. 151
Phase-Space Reconstruction - Singular System Approachp. 156
Estimating Dimensionsp. 158
How Many Points Are Enough?p. 162
Distinguishing Chaotic Signals from Nonchaotic or from Random Fractal Sequencesp. 173
Testing for Nonlinearityp. 177
Other Approaches to Estimate Dimensionsp. 178
Estimating the Lyapunov Exponents from Time Seriesp. 179
Evidence of Chaos in "Controlled" And "Uncontrolled" Experimentsp. 189
Chemical Experimentp. 189
Nonlinear Electrical Circuitsp. 193
Couette-Taylor Systemp. 194
Rayleigh-Benard Convectionp. 196
Other Experimentsp. 200
Do Low-Dimensional Attractors Exist in "Uncontrolled" Physical Systems?p. 202
Nonlinear Time Series Forecastingp. 213
Global and Local Approximationsp. 215
Examplesp. 222
Input-Output Systemsp. 224
Neural Networksp. 226
Examplesp. 231
Using Chaos in Weather Predictionp. 235
Chaos and Noisep. 238
Nonlinear Prediction as a Way of Distinguishing Chaotic Signals from Random Fractal Sequencesp. 241
Other Developments and Trends in the Application of Chaosp. 245
Shadowingp. 245
Noise Reductionp. 247
Statistical Noise Reductionp. 255
Some Additional Comments on the Effect of Truncation and Roundoff Error on Simulated Chaotic Trajectoriesp. 256
Control of Chaosp. 258
Referencesp. 259
Indexp. 271
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780306441714
ISBN-10: 0306441713
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 274
Published: 1992
Country of Publication: US
Dimensions (cm): 23.72 x 15.9  x 2.13
Weight (kg): 0.57