Measures of Complexity and Chaos

Front Matter....Pages i-x
Complexity and Chaos....Pages 1-27
Chaotic Metamorphoses....Pages 29-31
Measures of Dimensions from Astrophysical Data....Pages 33-49
Some Remarks on Nonlinear Data Analysis of Physiological Time Series....Pages 51-62
Hierarchies of Relations between Partial Dimensions and Local Expansion Rates in Strange Attractors....Pages 63-73
Experimental Study of the Multifractal Structure of the Quasiperiodic Set....Pages 75-78
Statistical Inference Theory for Measures of Complexity in Chaos Theory and Nonlinear Science....Pages 79-97
Practical Remarks on the Estimation of Dimension and Entropy from Experimental Data....Pages 99-110
Chaotic Behavior of the Forced Hodgkin-Huxley Axon....Pages 111-112
Chaotic Time Series Analysis Using Short and Noisy Data Sets: Application to a Clinical Epilepsy Seizure....Pages 113-116
Measuring Complexity in Terms of Mutual Information....Pages 117-119
Estimating Lyapunov Exponents from Approximate Return Maps....Pages 121-124
Estimating Local Intrinsic Dimensionality Using Thresholding Techniques....Pages 125-128
Seeking Dynamically Connected Chaotic Variables....Pages 129-132
On Problems Encountered with Dimension Calculations....Pages 133-136
Systematic Errors in Estimating Dimensions from Experimental Data....Pages 137-145
Analyzing Periodic Saddles in Experimental Strange Attractors....Pages 147-154
Time Evolution of Local Complexity Measures and Aperiodic Perturbations of Nonlinear Dynamical Systems....Pages 155-171
Analysis of Local Space/Time Statistics and Dimensions of Attractors Using Singular Value Decomposition and Information Theoretic Criteria....Pages 173-180
Entropy and Correlation Time in a Multimode Dye Laser....Pages 181-181
Dimension Calculation Precision with Finite Data Sets....Pages 183-186
Chaos in Childhood Epidemics....Pages 187-190
Measurements of f( α ) for Multifractal Attractors in Driven Diode Resonator Systems....Pages 191-192
“Is There a Strange Attractor in a Fluidized Bed ?”....Pages 193-197
Statistical Error in Dimension Estimators....Pages 199-202
Dynamical Complexity of Strange Sets....Pages 203-207
Characterization of Complex Systems by Aperiodic Driving Forces....Pages 209-212
Stabilization of Prolific Populations Through Migration and Long-Lived Propagules....Pages 213-218
Complex Behaviour of Systems Due to Semi-Stable Attractors: Attractors That Have Been Destabilized but which Still Temporarily Dominate the Dynamics of a System....Pages 219-223
Universal Properties of the Resonance Curve of Complex Systems....Pages 225-228
Effects of External Noise on Complexity in Two Dimensional Driven Damped Dynamical System....Pages 229-234
Chaos on a Catastrophe Manifold....Pages 235-240
Topological Frequencies in Dynamical Systems....Pages 241-243
Phase Transitions Induced by Deterministic Delayed Forces....Pages 245-248
Mutual Information Functions Versus Correlation Functions in Binary Sequences....Pages 249-252
Reduction of Complexity by Optimal Driving Forces....Pages 253-256
Symbolic Dynamical Resolution of Power Spectra....Pages 257-260
Relative Rotation Rates for Driven Dynamical Systems....Pages 261-263
Stretching Folding Twisting in the Driven Damped Duffing Device....Pages 265-268
Characterizing Chaotic Attractors Underlying Single Mode Laser Emission by Quantitative Laser Field Phase Measurement....Pages 269-280
Shil’nikov Chaos: How to Characterize Homoclinic and Heteroclinic Behaviour....Pages 281-294
Time Series Near Codimension Two Global Bifurcations....Pages 295-298
Characterization of Shilnikov Chaos in a CO 2 Laser Containing a Saturable Absorber....Pages 299-302
Symmetry Breaking Homoclinic Chaos....Pages 303-307
Time Return Maps and Distributions for the Laser with Saturable Absorber....Pages 309-312
Unfolding Complexity in Nonlinear Dynamical Systems....Pages 313-325
Inferring the Dynamic, Quantifying Physical Complexity....Pages 327-338
Symbolic Dynamics from Chaotic Time Series....Pages 339-343
Modelling Dynamical Systems from Real-World Data....Pages 345-348
Extraction of Models from Complex Data....Pages 349-358
Quantifying Chaos with Predictive Flows and Maps: Locating Unstable Periodic Orbits....Pages 359-366
Defect-Induced Spatio-Temporal Chaos....Pages 367-373
Lyapunov Exponents, Dimension and Entropy in Coupled Lattice Maps....Pages 375-379
Phase Dynamics, Phase Resetting, Correlation Functions and Coupled Map Lattices....Pages 381-394
Characterization of Spatiotemporal Structures in Lasers: A Progress Report....Pages 395-404
Amplitude Equations for Hexagonal Patterns of Convection in Non-Boussinesq Fluids....Pages 405-408
Fractal Dimensions in Coupled Map Lattices....Pages 409-424
Weak Turbulence and the Dynamics of Topological Defects....Pages 425-428
Pattern Cardinality as a Characterization of Dynamical Complexity....Pages 429-431
Characterizing Spatio-Temporal Chaos in Electrodeposition Experiments....Pages 433-443
Characterizing Space-Time Chaos in an Experiment of Thermal Convection....Pages 445-456
Characterizing Dynamical Complexity in Interfacial Waves....Pages 457-460
Characterization of Irregular Interfaces: Roughness and Self-Affine Fractals....Pages 461-464
The Field Patterns of a Hybrid Mode Laser: Detecting the “Hidden” Bistability of the Optical Phase Pattern....Pages 465-468
Back Matter....Pages 469-476