Extracting Knowledge From Time Series: An Introduction to Nonlinear Empirical Modeling
Mathematical modelling is ubiquitous. Almost every book in exact science touches on mathematical models of a certain class of phenomena, on more or less specific approaches to construction and investigation of models, on their applications, etc. As many textbooks with similar titles, Part I of our book is devoted to general qu- tions of modelling. Part II reffects our professional interests as physicists who spent much time to investigations in the field of non-linear dynamics and mathematical modelling from discrete sequences of experimental measurements (time series). The latter direction of research is known for a long time as “system identification” in the framework of mathematical statistics and automatic control theory. It has its roots in the problem of approximating experimental data points on a plane with a smooth curve. Currently, researchers aim at the description of complex behaviour (irregular, chaotic, non-stationary and noise-corrupted signals which are typical of real-world objects and phenomena) with relatively simple non-linear differential or difference model equations rather than with cumbersome explicit functions of time. In the second half of the twentieth century, it has become clear that such equations of a s-—ciently low order can exhibit non-trivial solutions that promise sufficiently simple modelling of complex processes; according to the concepts of non-linear dynamics, chaotic regimes can be demonstrated already by a third-order non-linear ordinary differential equation, while complex behaviour in a linear model can be induced either by random influence (noise) or by a very high order of equations.
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Extracting Knowledge From Time Series: An Introduction to Nonlinear Empirical Modeling
Mathematical modelling is ubiquitous. Almost every book in exact science touches on mathematical models of a certain class of phenomena, on more or less specific approaches to construction and investigation of models, on their applications, etc. As many textbooks with similar titles, Part I of our book is devoted to general qu- tions of modelling. Part II reffects our professional interests as physicists who spent much time to investigations in the field of non-linear dynamics and mathematical modelling from discrete sequences of experimental measurements (time series). The latter direction of research is known for a long time as “system identification” in the framework of mathematical statistics and automatic control theory. It has its roots in the problem of approximating experimental data points on a plane with a smooth curve. Currently, researchers aim at the description of complex behaviour (irregular, chaotic, non-stationary and noise-corrupted signals which are typical of real-world objects and phenomena) with relatively simple non-linear differential or difference model equations rather than with cumbersome explicit functions of time. In the second half of the twentieth century, it has become clear that such equations of a s-—ciently low order can exhibit non-trivial solutions that promise sufficiently simple modelling of complex processes; according to the concepts of non-linear dynamics, chaotic regimes can be demonstrated already by a third-order non-linear ordinary differential equation, while complex behaviour in a linear model can be induced either by random influence (noise) or by a very high order of equations.
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Extracting Knowledge From Time Series: An Introduction to Nonlinear Empirical Modeling
410
Extracting Knowledge From Time Series: An Introduction to Nonlinear Empirical Modeling
410Hardcover(2010)
$54.99
54.99
In Stock
Product Details
| ISBN-13: | 9783642126000 |
|---|---|
| Publisher: | Springer Berlin Heidelberg |
| Publication date: | 09/07/2010 |
| Series: | Springer Series in Synergetics |
| Edition description: | 2010 |
| Pages: | 410 |
| Product dimensions: | 6.30(w) x 9.20(h) x 1.10(d) |
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