This book provides a thorough review of a class of powerful algorithms 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. In particular, 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 emphasis is given to the much-disputed issue whether these algorithms can be successfully employed for the analysis of the human electroencephalogram.
Contents:
- Dynamical Systems, Time Series and Attractors
- Linear Methods
- State Space Reconstruction: Theoretical Foundations
- State Space Reconstruction: Practical Application
- Dimensions: Basic Definitions
- Lyapunov Exponents and Entropies
- Numerical Estimation of the Correlation Dimension
- Sources of Error and Data Set Size Requirements
- Monte Carlo Analysis of Dimension Estimation
- Surrogate Data Tests
- Dimension Analysis of the Human EEG
- Testing for Determinism in Time Series
Readership: Graduates and scientists in physics, applied mathematics, neurology, theoretical biology, economics, meteorology and neuroinformatics.
