Topics in Nonlinear Time Series Analysis:With Implications for EEG Analysis

    This book provides a thorough review of a class of powerful algorthms for the numerical analysis of complex time series data which were obtained from dynamical systems.These algorithms are based on the concept of state space representations of the underlying dynamics.as introduced by nonlinear dynamics.Inparticular.current algorithms for state space reconstruction.correlation dimension estimation.testing for determinism and surrogate data testing are presented-algorithms which have been playing a central role in the investigation of deterministic chaos and related phenomena since 1980.Special cmphasis is given to the much-disputed issue whether these algorithms can be successfully employed for the analysis of the human electroencephalogram.

Preface
Chapter 1 Introduction
1.1 Linearity and the beginning of time series analysis
1.2 Irregular time series and determinism
1.3 The objective of nonlinear time series analysis
1.4 Outline of the organisation of the present study
Chapter 2 Dynamical systems,time series and attractors
2.1 Overview
2.2 Dynamical systems and state spaces
2.3 Measurements and time series
2.4 Deterministic dynamical systems
　　2.4.1 Attractors
　　2.4.2 Linear systems
　　2.4.3 Invariant measures
　　2.4.4 Sensitive dependence on initial conditions
　　2.4.5 Maps and discretised flows
　　2.4.6 Some important maps
　　2.4.7 Some important flows
　2.5 Stochastic dynamical systems
　　2.5.1 Pure noise time series
　　2.5.2 Noise in dynamical systems
　　2.5.3 Linear stochastic systems
　2.6 Nonstationarity
　　……
Chapter 3 Linear methods
Chapter 4 State Space Reconstruction:Theoretical founda-tions
Chapter 5 State space resconstruction:Practical application
Chapter 6 Dimensions:Basic definitions
Chapter 7 Lyapunov exponents and entropies
Chapter 8 Numerical estimation of the correlation dimen-sion
Chapter 9 Sources of error and data set size requirements
Chapter 10 Monte Carlo analysis of dimension estimation
Chapter 11 Surrogate data tests
Chapter 12 Dimension analysis of the human EEG
Chapter 13 Testing for determinism in time series
Chapter 14 Conclusion