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Product Details: Coping with Chaos
| Author: | Edward Ott |
| Edited by: | Tim Sauer, James A. Yorke, James A. Yorke |
| Format: | Hardcover: Illustrated: 432 pages. |
| Publisher: | John Wiley & Sons (04/01/1994) |
| ISBN: | 0471025569 |
| ISBN13: | 9780471025566 |
| Reading Level: |
Publisher Notes: Coping with Chaos
Preface 1 Introduction to Chaos 2 2 Dimension 14 3 Symbolic Dynamics 24 4 Lyapunov Exponents and Entropy 31 5 The Theory of Embedding 41 6 The Practice of Embedding 65 Geometry from a time series
by N. Packard, J. Crutchfield, D. Farmer, R. Shaw68 Extracting qualitative dynamics from experimental data
by D. S. Broomhead, G. P. King72 Determining embedding dimension for phase-space reconstruction using a geometrical construction
by M. Kennel, R. Brown, H. Abarbanel92 Direct test for determinism in a time series
by D. Kaplan, L. Glass101 7 Dimension Calculations 105 Singular-value decomposition and the Grassberger-Procaccia algorithm
by A. M. Albano, J. Muench, C. Schwartz, A. I. Mees, P. E. Rapp107 Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems
by J.-P. Eckmann, D. Ruelle117 Plateau onset for correlation dimension: When does it occur?
by M. Ding, C. Grebogi, E. Ott, T. Sauer, J. A. Yorke120 Testing for nonlinearity in time series: The method of surrogate data
by J. Theiler, S. Eubank, A. Longtin, B. Galdrakian, J. D. Farmer124 Strange attractors in weakly turbulent Couette-Taylor flow
by A. Brandstater, H. L. Swinney142 Dimension measurements for geostrophic turbulence
by J. Guckenheimer, G. Buzyna156 8 Calculation of Lyapunov Exponents 160 Liapunov exponents from time series
by J.-P. Eckmann, S. O. Kamphorst, D. Ruelle, S. Ciliberto162 Lyapunov exponents from observed time series
by P. Bryant, R. Brown, H. Abarbanel171 Identification of true and spurious Lyapunov exponents from time series
by U. Parlitz175 9 Periodic Orbits and Symbolic Dynamics 186 Characterization of an experimental strange attractor by periodic orbits
by D. P. Lathrop, E. J. Kostelich187 Model identification by periodic-orbit analysis for NMR-laser chaos
by L. Flepp, R. Holzner, E. Brun, M. Finardi, R. Badii191 Experimental confirmation of the theory for critical exponents of crises
by J. C. Sommerer, W. L. Ditto, C. Grebogi, E. Ott, M. Spano195 Structure of chaos in the laser with saturable absorber
by F. Papoff, A. Fioretti, E. Arimondo, G. B. Mindlin, H. Solari, R. Gilmore200 10 Prediction 206 Predicting chaotic time series
by J. D. Farmer, J. Sidorowich208 Nonlinear prediction of chaotic time series
by M. Casdagli212 Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series
by G. Sugihara, R. M. May234 Time series prediction using delay coordinate embedding
by T. Sauer241 11 Noise Reduction 261 Noise reduction in dynamical systems
by E. J. Kostelich, J. A. Yorke263 On noise reduction methods for chaotic data
by P. Grassberger, R. Hegger, H. Kantz, C. Schaffrath, T. Schreiber267 A noise reduction method for chaotic systems
by S. Hammel282 12 Control: Theory of Stabilization of Unstable Orbits 290 Controlling chaos
by E. Ott, C. Grebogi, J. A. Yorke292 Controlling chaos using time delay coordinates
by U. Dressler, G. Nitsche296 Controlling chaotic dynamical systems
by F. Romeiras, C. Grebogi, E. Ott, W. P. Dayawansa300 Bifurcation control of chaotic dynamical systems
by H. Wang, E. H. Abed328 13 Control: Experimental Stabilization of Unstable Orbits 334 Experimental control of chaos
by W. Ditto, S. N. Rauseo, M. L. Spano336 Controlling a chaotic system
by J. Singer, Y.-Z. Wang, H. H. Bau340 Controlling cardiac chaos
by A. Garfinkel, M. Spano, W. Ditto, J. Weiss343 Stabilizing high-period orbits in a chaotic system: The diode resonator
by E. R. Hunt349 Tracking unstable steady states: Extending the stability regime of a multimode laser system
by Z. Gills, C. Iwata, R. Roy, I. Schwartz, I. Triandaf352 Controlling chaos in the Belousov-Zhabotinsky reaction
by V. Petrov, V. Gaspar, J. Masere, K. Showalter356 14 Control: Targeting and Goal Dynamics 360 Using the sensitive dependence of chaos (the "butterfly effect") to direct trajectories in an experimental chaotic system
by T. Shinbrot, W. Ditto, C. Grebogi, E. Ott, M. Spano, J. A. Yorke361 Resonant stimulation and control of nonlinear oscillators
by A. Hubler, E. Luscher365 The entrainment and migration controls of multiple-attractor systems
by E. A. Jackson368 15 Synchronism and Communication 375 Synchronization in chaotic systems
by L. M. Pecora, T. L. Carroll377 Circuit implementation of synchronized chaos with applications to communication
by K. M. Cuomo, A. V. Oppenheim381 Communicating with chaos
by S. Hayes, C. Grebogi, E. Ott385 Observing chaos: Deducing and tracking the state of a chaotic system from limited observation
by P. So, E. Ott, W. P. Dayawansa389 Bibliography 396 Index 415
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