Measures of Complexity and Chaos

30.06.1990

Englisch

9780306433870

Springer US

NATO Science Series: B

Nein

486

1989

Gebundene Ausgabe

208

Signal, development, Counter, bifurcation, chaos, dynamical systems, entropy, modeling, Diode, Phase, complexity, laser

THR - Elektrotechnik PHU - Mathematische Physik

Complexity and Chaos.- Chaotic Metamorphoses.- I. Characterizing Temporal Complexity: Chaos.- A. Measuring Dimensions, Entropies and Lyapunov Exponents.- Measures of Dimensions from Astrophysical Data.- Some Remarks on Nonlinear Data Analysis of Physiological Time Series.- Hierarchies of Relations Between Partial Dimensions and Local Expansion Rates in Strange Attractors.- Experimental Study of the Multifractal Structure of the Quasiperiodic Set.- Statistical Inference Theory for Measures of Complexity in Chaos Theory and Nonlinear Science.- Practical Remarks on the Estimation of Dimension and Entropy from Experimental Data.- Chaotic Behavior of the Forced Hodgkin-Huxley Axon.- Chaotic Time Series Analysis Using Short and Noisy Dta Sets: Applications to a Clinical Epilepsy Seizure.- Measuring Complexity in Terms of Mutual Information.- Estimating Lyapunov Exponents From Approximate Return Maps.- Estimating Local Intrinsic Dimensionality Using Thresholding Techniques.- Seeking Dynamically Connected Chaotic Variables.- On Problems Encountered with Dimension Calculations.- Systematic Errors in Estimating Dimensions from Experimental Data.- Analyzing Periodic Saddles in Experimental Strange Attractors.- Time Evolution of Local Complexity Measures and Aperiodic Perturbations of Nonlinear Dynamical Systems.- Analysis of Local Space/Time Statistics and Dimensions of Attractors Using Singular Value Decompositon and Information Theoretic Criteria.- Entropy and Correlation Time in a Multimode Dye Laser.- Dimension Calculation Precision with Finite Data Sets.- Chaos in Childhood Epidemics.- Measurement of f(?) for Multifractal Attractors in Driven Diode Resonator Systems.- Is there a Strange Attractor in a Fluidized Bed?.- Statistical Error in Dimension Estimators.- B. Other Measures.- Dynamical Complelxity of Strange Sets.- Characterization of Complexity by Aperiodic Driving Forces.- Stabilization of Prolific Populations Through Migration and Long-lived Propagules.- Complex Behavior of Systems Due to Semi-stable Attractors: Attractors That Have Been Destablized but Which Still Temporarily Dominate the Dynamics of a System.- Universal Properties of the Resonance Curve of Complex Systems.- The Effects of External Noise on Complexity in Two-dimensional Driven Damped Dynamical System.- Chaos on a Catastrophe Manifold.- Topolgical Frequencies in Dynamical Systems.- Phase Transitions Induced by Deterministic Delayed Forces.- Mutual Information Functions Versus Correlation Functions in Binary Sequences.- Reduction of Complexity by Optimal Driving Forces.- Symbolic Dynamical Resolution of Power Spectra.- Relative Rotation Rates for Driven Dynamical Systems.- Stretching Folding Twisting in the Driven Damped Duffing Device.- Characterizing Chaotic Attractors Underlying Single Mode Laser Emission by Quantitative Laser Field Phase Measurements.- C. Characterizing Homoclinic Chaos.- Shil’nikov Chaos: How to Characterize Homoclinic and Heteroclinic Behavior.- Time Series Near Codimension Two Global Bifurcations.- Characterization of Shil’nikov Chaos in a CO2 Laser Containing a Saturable Absorber.- Symmetry-breaking Homoclinic Chaos.- Time Return Maps and Distributions for the Laser with Saturable Absorber.- D. Building Models from Data.- Unfolding Complexity in Nonlinear Dynamical Systems.- Inferring the Dynamic; Quantifying Physical Complexity.- Symbolic Dynamics from Chaotic Time Series.- Modelling Dynamical Systems from Real-world Data.- Extraction of Models from Complex Data.- Quantifying Chaos with Predictive Flows and Maps: Locating Unstable Periodic Orbits.- II. Characterizing Spatio- Temp Oral Complexity: Turbulence.- A. Theoretical.- Defect-induced Spatio-temporal Chaos.- Lyapunov Exponents, Dimension and Entropy in Coupled Lattice Maps.- Phase Dynamics, Phase Resettiing, Correlation Functions and Coupled Map Lattices.- Characterization of Spatiotemporal Structures in Lasers: A Progress Report.- Amplitude Equations for Hexagonal Patterns of Convection in Non-Boussinesq Fluids.- Fractal Dimensions in Coupled Map Lattices.- Weak Turbulence and the Dynamics of Topological Defects.- Pattern Cardinality as a Characterization of Dynamical Complexity.- B. Experimental.- Characterizing Spatiotemporal Chaos in Electrodeposition Experiments.- Characterizing Space-time Chaos in an Experiment of Thermal Convection...- Characterizing Dynamical Complexity in Interfacial Waves.- Characterization of Irregular Interfaces: Roughness and Self-affine Fractals.- The Field Patterns of a Hybrid Mode Laser: Detecting the “Hidden” Bistability of the Optical Phase Pattern.- Contributors.

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