Extracting Knowledge From Time Series An Introduction to Nonlinear Empirical Modeling - Bezruchko, Boris P.; Smirnov, Dmitry A.; SpringerLink (Online service) (Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2010)
This book addresses the fundamental question of how to construct mathematical models for the evolution of dynamical systems from experimentally-obtained time series. It places emphasis on chaotic signals and nonlinear modeling and discusses different approaches to the forecast of future system evolution. In particular, it teaches readers how to construct difference and differential model equations depending on the amount of a priori information that is available on the system in addition to the experimental data sets. This book will benefit graduate students and researchers from all natural sciences who seek a self-contained and thorough introduction to this subject.
Models And Forecast -- The Concept of Model. What is Remarkable in Mathematical Models -- Two Approaches to Modelling and Forecast -- Dynamical (Deterministic) Models of Evolution -- Stochastic Models of Evolution -- Modeling From Time Series -- Problem Posing in Modelling from Data Series -- Data Series as a Source for Modelling -- Restoration of Explicit Temporal Dependencies -- Model Equations: Parameter Estimation -- Model Equations: Restoration of Equivalent Characteristics -- Model Equations: (3z(BBlack Box(3y (BReconstruction -- Practical Applications of Empirical Modelling -- Identification of Directional Couplings -- Outdoor Examples.s
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