Section I: 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; Section II: 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; Section III: 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
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.
A state-of-the-art edited survey of the theory and methods used for nonlinear time series analysis. Professionals, researchers, and graduates in nonlinear dynamics, probability, optimization, and systems theory will find the book useful.