상세정보

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.

정보제공 :

CONTENTS
Preface = xi
PART Ⅰ Background
 1. Introduction to Chaos = 2
  1.1 Dynamical systems = 2
  1.2 Attractors = 5
  1.3 Chaos = 9
 2. Dimension = 14
  2.1 Natural measure = 14
  2.2 The spectrum of D_q dimensions = 15
  2.3 Properties of the information dimension = 17
  2.4 An example : The generalized baker's map = 18
  2.5 The singularity spectrum $$f(\alpha )$$ = 21
 3. Symbolic Dynamics = 24
  3.1 Itineraries = 24
  3.2 Symbolic dynamics = 26
 4. Lyapunov Exponents and Entropy = 31
  4.1 Lyapunov exponents = 31
  4.2 Baker's map example = 34
  4.3 Numerical calculation of Lyapunov exponents = 35
  4.4  Lyapunov dimension = 36
  4.5 Entropy = 37
 5. The Theory Embedding = 41
  5.1 Measurements and state representation = 42
  5.2 Topological embedding = 44
  5.3 Delay coordinates = 50
  5.4 Differentiable embeddings = 54
  5.5 Embedding of filtered data = 56
PART Ⅱ Analysis of Data from Chaotic Systems
 6. The Practice of Embedding = 65
  Editor's Notes = 65
  Geometry from a time series / N. Packard ; J. Crutchfied ; D. Farmer ; R. Shaw = 68
  Extracting qualitative dynmics from experimental data / D.S. Broomhead ; G.P. King = 72
  Determining embedding dimension for phase-space reconstruction using a geometrical construction / M. Kennel ; R. Brown ; H. Abarbanel = 92
  Direct test for determinism in a time series / D. Kaplan ; L. Glass = 101
 7. Dimension Calculations = 105
  Editor's Notes = 105
  Singular-value decomposition and the Grassberger-Procaccia algorithm / A.M. Albano ; J. Muench ; C. Schwartz ; A.I. Mees ; P.E. Rapp = 107
  Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems / J.-P. Echmann ; D. Ruelle = 117
  Plateau onset for correlation dimension: When does it occur? / M. Ding ; C. Grebogi ; E. Ott ; T. Sauer ; J.A. Yorke = 120
  Testing for nonlinearity in time series: The method of surrogate data / J. Theiler ; S. Eubank ; A. Longtin ; B. Galdrakian ; J.D. Farmer = 124
  Strange attractors in weakly turbulent Couette-Taylor flow / A. Brandstater ; H.L. Swinney = 142
  Dimension measurements for geostrophic turbulence / J. Guckenheimer ; G. Buzyna = 156
 8. Calculation of Lyapunov Exponents = 160
  Editor's Notes = 160
  Liapunov exponents from series / J.-P. Eckmann ; S.O. Kamphorst ; D. Ruelle ; S. Ciliberto = 162
  Liapunov exponents from observed time series / P. Bryant ; R. Brown ; H. Abarbanel = 171
  Identification of true and spurious Liapunov exponents from time series / U. Parlitz = 175
 9. Periodic Orbits and Symbolic Dynamics = 186
  Editor's Notes = 186
  Characterization of an experimental strang attractor by periodic orbits / D.P. Lathrop ; K.J. Kostelich = 187
  Model identification by periodic-orbit analysis for NMR-laser chaos / L. Flepp ; R. Holzner ; E. Brun ; M. Finardi ; R. Badii = 191
  Experimental confirmation of the theory for critical exponents of crises / J.C. Sommerer ; W.L. Ditto ; C. Grebogi ; E. Ott ; M. Spano = 195
  Structure of chaos in the laser with saturable absorber / F. Papoff ; A. Fioretti ; E. Arimondo ; G.B. Mindlin ; H. Solari ; R. Gilmore = 200
PART Ⅲ Prediction, Filtering, Control and Communication in Chaotic Systems
 10. Prediction = 206
  Editor's Notes = 206
  Predicting chaotic time series / J.D. Farmer ; J. Sidorowich = 208
  Nonlinear prediction of chaotic time series / M. Casdagli = 212
  Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series / G. Sugihara ; R.M. May = 234
  Time series prediction using delay coordinate embedding / T. Sauer = 241
 11. Noise Reduction = 261
  Editor's Notes = 261
  Noise reduction in dynamical systems / E.J. Kostelich ; J.A. Yorke = 263
  On noise reduction methods for chaotic data / P. Grassberger ; R. Hegger ; H. Kantz ; C. Schaffrath ; T. Schreiber = 267
  A noise reduction method for chaotic systems / S. Hammel = 282
 12. Control: Theory of Stabilization of Unstable Orbits = 290
  Editor's Notes = 290
  Controlling chaos / E. Ott ; C. Grebogi ; J.A. Yorke = 292
  Controlling chaos using time delay coordinates / U. Dressler ; G. Nitsche = 296
  Controlling chaotic dynamical systems / F. Romeiras ; C. Grebogi ; E. Ott ; W.P. Dayawansa = 300
  Bifurcation control of chaotic dynamical systems / H. Wang ; E.H. Abed = 328
 13. Control: Experimental Stabilization of Unstable Orbits = 334
  Editor's Notes = 334
  Experimental control of chaos / W. Ditto ; S. N. Rauseo ; M. L. Spano = 336
  Controlling a chaotic system / J. Singer ; Y. -Z. Wang ; H. H. Bau = 340
  Controlling cardiac chaos / A. Garfinkel ; M. Spano ; W. Ditto ; J. Weiss = 343
  Stabilizing high-period orbits in a chaotic system : The diode resonator / E.R. Hunt = 349
  Tracking unstable steady states: Extending the stability regime of a multimode laser system / Z. Gills ; C. Iwata ; R. Roy ; I. Schwartz ; I. Triandaf = 352
  Controlling chaos in the Belousov-Zhabotinsky reaction / V. Petrov ; V. Gaspar ; J. Masere ; K. Showalter = 356
 14. Control: Targeting and Goal Dynamics = 360
  Editor's Notes = 360
  Using the sensitive dependence of chaos (the "butterfly effect") to direct trajectories in an experimental chaotic system / T. Shinbrot ; W. Ditto ; C. Grebogi ; E. Ott ; M. Spano ; J.A. Yorke = 361
  Resonant stimulation and control of nonlinear oscillators / A. H$$\ddot u$$bler ; E. L$$\ddot u$$sher = 365
  The entrainment and migration controls of multiple - attractor systems / E. A. Jackson = 368
 15. Synchronism and Communication = 375
  Editor's Notes = 375
  Synchronization in chaotic systems / L.M. Pecora ; T.L. Carroll = 377
  Circuit implementation of synchronized chaos with applications to communication / K.M. Cuomo ; A. V. Oppenheim = 381
  Communicating with chaos / S. Hayes ; C. Grebogi ; E. Ott = 385
  Observing chaos : Deducing and tracking the state of a chaotic system from limited observation / P. So ; E. Ott ; W. P. Dayawansa = 389
 Bibliography = 396
 Index = 415