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Extracting Knowledge From Time Series - An Introduction to Nonlinear Empirical Modeling (Paperback, 2010 ed.)
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Extracting Knowledge From Time Series - An Introduction to Nonlinear Empirical Modeling (Paperback, 2010 ed.)
Series: Springer Series in Synergetics
Expected to ship within 18 - 22 working days
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Mathematical modelling is ubiquitous. Almost every book in exact
science touches on mathematical models of a certain class of
phenomena, on more or less speci?c 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 re?ects our professional
interests as physicists who spent much time to investigations in
the ?eld 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
identi?cation" 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 suf?ciently 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
in?uence (noise) or by a very high order of equations.
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