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Analysis of observed chaoti...
This book develops a clear and systematic treatment of time series of data, regular and chaotic, that one finds in observations of nonlinear systems. The reader is led from measurements of one or more variables through the steps of building models of the source as a dynamical system, classifying the source by its dynamical characteristics, and finally predicting and controlling the dynamical system. The text examines methods for separating the signal of physical interest from contamination by unwanted noise, and for investigating the phase space of the chaotic signal and its properties. The emphasis throughout is on the use of the modern mathematical tools for investigating chaotic behavior to uncover properties of physical systems. The methods require knowledge of dynamical systems at the advanced undergraduate level and some knowledge of Fourier transforms and other signal processing methods. The toolkit developed in the book will provide the reader with efficient and effective methods for analyzing signals from nonlinear sources; these methods are applicable to problems of control, communication, and prediction in a wide variety of systems encountered in physics, chemistry, biology, and geophysics
Monografía
monografia Rebiun22059186 https://catalogo.rebiun.org/rebiun/record/Rebiun22059186 m o d cr bn||||||abp cr bn||||||ada 101110s1996 nyua ob 001 0 eng d 625926403 853269824 958524303 1001479591 1012482162 9781461207634 1461207630 0387945237 hardcover ; alk. paper) 9780387945231 hardcover ; alk. paper) 0387983724 pbk.) 9780387983721 pbk.) 10.1007/978-1-4612-0763-4 doi AU@ 000051746243 NZ1 14980338 NZ1 15621351 AU@ 000057641893 OCLCE eng pn OCLCE OCLCQ OCLCF OCLCO UA@ AU@ GW5XE COO OCLCQ EBLCP YDX UAB OCLCO OCLCQ OCLCO dlr 501/.1385 20 30.99 bcl Abarbanel, H. D. I. Analysis of observed chaotic data Henry D.I. Abarbanel New York Springer ©1996 New York New York Springer 1 online resource (xiv, 272 pages) illustrations 1 online resource (xiv, 272 pages) Text txt rdacontent computer c rdamedia online resource cr rdacarrier Institute for Nonlinear Science 1431-4673 Includes bibliographical references (pages 261-268) and index 1 Introduction -- 1.1 Chatter in Machine Tools -- 2 Reconstruction of Phase Space -- 2.1 Observations of Regular and Chaotic Motions -- 2.2 Chaos in Continuous and Discrete Time Dynamics -- 2.3 Observed Chaos -- 2.4 Embedding: Phase Space Reconstruction -- 2.5 Reconstruction Demystified -- 3 Choosing Time Delays -- 3.1 Prescriptions for a Time Delay -- 3.2 Chaos as an Information Source -- 3.3 Average Mutual Information -- 3.4 A Few Remarks About I(T) -- 4 Choosing the Dimension of Reconstructed Phase Space -- 4.1 Global Embedding Dimension dE -- 4.2 Global False Nearest Neighbors -- 4.3 A Few Remarks About Global False Nearest Neighbors -- 4.4 False Strands -- 4.5 Other Methods for Identifying dE -- 4.6 The Local or Dynamical Dimension dL -- 4.7 Forward and Backward Lyapunov Exponents -- 4.8 Local False Neighbors -- 4.9 A Few Remarks About Local False Nearest Neighbors -- 5 Invariants of the Motion -- 5.1 Invariant Characteristics of the Dynamics -- 5.2 Fractal Dimensions -- 5.3 Global Lyapunov Exponents -- 5.4 Lyapunov Dimension -- 5.5 Global Lyapunov Exponents from Data -- 5.6 Local Lyapunov Exponents -- 5.7 Local Lyapunov Exponents from Data -- 5.8 A Few Remarks About Lyapunov Exponents -- 6 Modeling Chaos -- 6.1 Model Making in Chaos -- 6.2 Local Models -- 6.3 Global Models -- 6.4 Phase Space Models for Dependent Dynamical Variables -- 6.5 'Black Boxes' and Physics -- 7 Signal Separation -- 7.1 General Comments -- 7.2 Full Knowledge of the Dynamics -- 7.3 Knowing a Signal: Probabilistic Cleaning -- 7.4 'Blind' Signal Separation -- 7.5 A Few Remarks About Signal Separation -- 8 Control and Chaos -- 8.1 Parametric Control to Unstable Periodic Orbits -- 8.2 Other Controls -- 8.3 Examples of Control -- 8.4 A Few (Irreverent) Remarks About Chaos and Control -- 9 Synchronization of Chaotic Systems -- 9.1 Identical Systems -- 9.2 Dissimilar Systems -- 9.3 Mutual False Nearest Neighbors -- 9.4 Predictability Tests for Generalized Synchronization -- 9.5 A Few Remarks About Synchronization -- 10 Other Example Systems -- 10.1 Chaotic Laser Intensity Fluctuations -- 10.2 Chaotic Volume Fluctuations of the Great Salt Lake -- 10.3 Chaotic Motion in a Fluid Boundary Layer -- 11 Estimating in Chaos: Cramér-Rao Bounds -- 11.1 The State Estimation Problem -- 11.2 The Cramér-Rao Bound -- 11.3 Symmetric Linear Dynamics -- 11.4 Arbitrary, Time-Invariant, Linear Systems -- 11.5 Nonlinear, Chaotic Dynamics -- 11.6 Connection with Chaotic Signal Separation -- 11.7 Conclusions -- 12 Summary and Conclusions -- 12.1 The Toolkit-Present and Future -- 12.2 Making 'Physics' out of Chaos-Present and Future -- 12.3 Topics for the Next Edition -- A.1 Information Theory and Nonlinear Systems -- A.2 Stability and Instability -- A.2.1 Lorenz Model -- References Use copy. Restrictions unspecified star. MiAaHDL This book develops a clear and systematic treatment of time series of data, regular and chaotic, that one finds in observations of nonlinear systems. The reader is led from measurements of one or more variables through the steps of building models of the source as a dynamical system, classifying the source by its dynamical characteristics, and finally predicting and controlling the dynamical system. The text examines methods for separating the signal of physical interest from contamination by unwanted noise, and for investigating the phase space of the chaotic signal and its properties. The emphasis throughout is on the use of the modern mathematical tools for investigating chaotic behavior to uncover properties of physical systems. The methods require knowledge of dynamical systems at the advanced undergraduate level and some knowledge of Fourier transforms and other signal processing methods. The toolkit developed in the book will provide the reader with efficient and effective methods for analyzing signals from nonlinear sources; these methods are applicable to problems of control, communication, and prediction in a wide variety of systems encountered in physics, chemistry, biology, and geophysics Electronic reproduction. [S.l.] HathiTrust Digital Library 2010. MiAaHDL Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL digitized 2010 HathiTrust Digital Library committed to preserve pda MiAaHDL Chaotic behavior in systems Chaotic behavior in systems Sistemas especificos (teoria de controle) Zustandsraum Nichtlineares System Chaotisches System Zeitreihenanalyse Electronic books Print version Abarbanel, H.D.I. Analysis of observed chaotic data. New York : Springer, ©1996 (DLC) 95018641 (OCoLC)32469054 Institute for Nonlinear Science 1431-4673