Analysis of Observed Chaotic Data

1. Auflage 1995
ISBN: 978-0-387-94523-1
Verlag: Springer Nature B.V.

Buch, Englisch, 288 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 600 g

Reihe: Institute for Nonlinear Science

A clear and systematic treatment of time series of data, regular and chaotic, found in nonlinear systems. The text leads readers from measurements of one or more variables through the steps of building models of the source as a dynamical system, classifying the source by its dynamical characteristics, and finally predicting and controlling the dynamical system. It examines methods for separating the signal of physical interest from contamination by unwanted noise, and for investigating the phase space of the chaotic signal and its properties. The emphasis throughout is on the use of modern mathematical tools for investigating chaotic behaviour to uncover properties of physical systems, requiring knowledge of dynamical systems at the advanced undergraduate level and some knowledge of Fourier transforms and other signal processing methods.

Zielgruppe

Graduate

Autoren/Hrsg.

Abarbanel, Henry D.I.

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

Regular Dynamics: Newton to Poincaré; KAM Theorem Bifurcations: Routes to Chaos, Stability and Instability Reconstruction of Phase Space: Regular and Chaotic Motions; Observed Chaos Choosing Time Delays: Chaos as an Information Source; Average Mutual Information. Choosing the Dimension of Reconstructed Phase Space Invariants of the Motion: Global & Local Lyapunov Exponents; Lorenz Model Modeling Chaos: Local & Global Models; Phase Space Models Signal Separation: Probabilistic Cleaning; "Blind" Signal Separation Control and Chaos: Parametric Control; Examples of Control (including magnetoelastic ribbon, electric circuits, cardiac tissue) Synchronization of Chaotic Systems: Identical or Dissimilar Systems; Chaotic Nonlinear Circuits Other Example Systems: Laser Intensity Fluctuations; Volume Fluctuations of the Great Salt Lake; Motion in a Fluid Boundary Layer Estimating in Chaos: Cramér-Rao Bounds The Chaos Toolkit: Making "Physics" out of Chaos