Nonlinear Time Series Analysis

New edition of a successful advanced text on nonlinear time series analysis.

Holger Kantz (Author), Thomas Schreiber (Author)

9780521529020, Cambridge University Press

Paperback, published 27 November 2003

388 pages, 118 b/w illus. 4 tables 43 exercises
24.6 x 17 x 2.3 cm, 0.66 kg

'… a very readable introduction to the concepts and clear descriptions of the techniques, as well as cautions, where appropriate, about potential pitfalls and misuses of the methods. … the book is a good reference to the current state of the art from the nonlinear dynamics community and is important reading for anyone faced with interpreting irregular time series.' Contemporary Physics

The paradigm of deterministic chaos has influenced thinking in many fields of science. Chaotic systems show rich and surprising mathematical structures. In the applied sciences, deterministic chaos provides a striking explanation for irregular behaviour and anomalies in systems which do not seem to be inherently stochastic. The most direct link between chaos theory and the real world is the analysis of time series from real systems in terms of nonlinear dynamics. Experimental technique and data analysis have seen such dramatic progress that, by now, most fundamental properties of nonlinear dynamical systems have been observed in the laboratory. Great efforts are being made to exploit ideas from chaos theory wherever the data displays more structure than can be captured by traditional methods. Problems of this kind are typical in biology and physiology but also in geophysics, economics, and many other sciences.

Preface
Acknowledgements
Part I. Basic Topics: 1. Introduction: why nonlinear methods?
2. Linear tools and general considerations
3. Phase space methods
4. Determinism and predictability
5. Instability: Lyapunov exponents
6. Self-similarity: dimensions
7. Using nonlinear methods when determinism is weak
8. Selected nonlinear phenomena
Part II. Advanced Topics: 9. Advanced embedding methods
10. Chaotic data and noise
11. More about invariant quantities
12. Modelling and forecasting
13. Non-stationary signals
14. Coupling and synchronisation of nonlinear systems
15. Chaos control
Appendix A: using the TISEAN programs
Appendix B: description of the experimental data sets
References
Index.

Subject Areas: Physics [PH], Nonlinear science [PBWR]