Nonlinear Dynamics and Statistics

By: Alistair I. Mees (Editor)

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Hardcover | 1 February 2001

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Hardcover
496 Pages

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23.5 x 15.88 x 2.54

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Recently, a great deal of progress has been made in the modeling and understanding of processes with nonlinear dynamics, even when only time series data are available. Modern reconstruction theory deals with creating nonlinear dynamical models from data and is at the heart of this improved understanding. Most of the work has been done by dynamicists, but for the subject to reach maturity, statisticians and signal processing engineers need to provide input both to the theory and to the practice. The book brings together different approaches to nonlinear time series analysis in order to begin a synthesis that will lead to better theory and practice in all the related areas. This book describes the state of the art in nonlinear dynamical reconstruction theory. The chapters are based upon a workshop held at the Isaac Newton Institute, Cambridge University, UK, in late 1998. The book's chapters present theory and methods topics by leading researchers in applied and theoretical nonlinear dynamics, statistics, probability, and systems theory. Features and topics: * disentangling uncertainty and error: the predictability of nonlinear systems * achieving good nonlinear models * delay reconstructions: dynamics vs. statistics * introduction to Monte Carlo Methods for Bayesian Data Analysis * latest results in extracting dynamical behavior via Markov Models * data compression, dynamics and stationarity Professionals, researchers, and advanced graduates in nonlinear dynamics, probability, optimization, and systems theory will find the book a useful resource and guide to current developments in the subject.

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Paperback

Published: 5th November 2012

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Issues in Reconstructing Dynamics
Challenges in Modeling Nonlinear Systems: A Worked Example
Disentangling Uncertainty and Error: On the Predictability of Nonlinear Systems
Achieving Good Nonlinear Models: Keep it Simple, Vary the Embedding, and Get the Dynamics Right
Delay Reconstruction: Dynamics vs. Statistics
Some Remarks on the Statistical Modelling of Chaotic Systems
The Identification and Estimation of Nonlinear Stochastic Systems
Fundamentals
An Introduction to Monte Carlo Methods for Bayesian Data Analysis
Contrained Randomization of Time Series For Nonlinearity Tests
Removing the Noise from Chaos Plus Noise
Embedding Theorems, Scaling Structures, and Determinism in Time Series
Consistent Estimation of a Dynamical Map
Extracting Dynamical Behaviour via Markov Models
Formulas for the Eckmann-Ruelle Matrix
Methods and Applications
Noise and Nonlinearity in an Ecological System
Cluster-Weighted Modeling: Probabilistic Time Series Prediction, Characterization and Synthesis
Data Compression, Dynamics and Stationarity
Analyzing Nonlinear Dynamical Systems with Nonparametric Regression
Optimization of Embedding Parameters for Prediction of Seizure Onset with Mutual Information
Detection of a Nonlinear Oscillator Underlying Experimental Time Series: The Sunspot Cycle
Table of Contents provided by Publisher. All Rights Reserved.

Nonlinear Dynamics and Statistics

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Hardcover

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