Nonlinear time series analysis
著者
書誌事項
Nonlinear time series analysis
Cambridge University Press, 2004, c2003
2nd ed
- : hard
- : pbk
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注記
First paperback edition (with correction) 1999; reprinted 1999, 2002
Includes bibliographical references (p. 350-363) and index
内容説明・目次
内容説明
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.
目次
- 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.
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