Coping with chaos : analysis of chaotic data and the exploitation of chaotic systems

목차 (Table of Contents)

• 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