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Nonlinear time series methods have developed rapidly over a quarter of a century and have reached an advanced state of maturity during the last decade. Implementations of these methods for experimental data are now widely accepted and fairly routine; however, genuinely useful applications remain rare. This book focuses on the practice of applying these methods to solve real problems.
To illustrate the usefulness of these methods, a wide variety of physical and physiological systems are considered. The technical tools utilized in this book fall into three distinct, but interconnected areas: quantitative measures of nonlinear dynamics, Monte-Carlo statistical hypothesis testing, and nonlinear modeling. Ten highly detailed applications serve as case studies of fruitful applications and illustrate the mathematical techniques described in the text.
Sample Chapter(s)
Chapter 1: Time series embedding and reconstruction (765 KB)
Contents:
- Times Series Embedding and Reconstruction
- Dynamics Measures and Topological Invariants
- Estimation of Correlation Dimension
- The Method of Surrogate Data
- Non-Standard and Nonlinear Surrogates
- Identifying the Dynamics
- Applications
Readership: Postgraduate students, researchers, academics and practitioners in nonlinear physics and in various other areas of potential application (e.g. engineering, biology and medicine).
