Analysis Of Observed Chaotic Data
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Analysis Of Observed Chaotic Data
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Author : Henry Abarbanel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Analysis Of Observed Chaotic Data written by Henry Abarbanel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
When I encountered the idea of chaotic behavior in deterministic dynami cal systems, it gave me both great pause and great relief. The origin of the great relief was work I had done earlier on renormalization group properties of homogeneous, isotropic fluid turbulence. At the time I worked on that, it was customary to ascribe the apparently stochastic nature of turbulent flows to some kind of stochastic driving of the fluid at large scales. It was simply not imagined that with purely deterministic driving the fluid could be turbulent from its own chaotic motion. I recall a colleague remarking that there was something fundamentally unsettling about requiring a fluid to be driven stochastically to have even the semblance of complex motion in the velocity and pressure fields. I certainly agreed with him, but neither of us were able to provide any other reasonable suggestion for the observed, apparently stochastic motions of the turbulent fluid. So it was with relief that chaos in nonlinear systems, namely, complex evolution, indistinguish able from stochastic motions using standard tools such as Fourier analysis, appeared in my bag of physics notions. It enabled me to have a physi cally reasonable conceptual framework in which to expect deterministic, yet stochastic looking, motions. The great pause came from not knowing what to make of chaos in non linear systems.
Analysis Of Observed Chaotic Data
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Author : Mehmet Emre Çek
language : en
Publisher:
Release Date : 2004
Analysis Of Observed Chaotic Data written by Mehmet Emre Çek and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Chaotic behavior in systems categories.
In this thesis, analysis of observed chaotic data has been investigated. The purpose of analyzing time series is to make a classification between the signals observed from dynamical systems. The classifiers are the invariants related to the dynamics. The correlation dimension has been used as classifier which has been obtained after phase space reconstruction. Therefore, necessary methods to find the phase space parameters which are time delay and the embedding dimension have been offered. Since observed time series practically are contaminated by noise, the invariants of dynamical system can not be reached without noise reduction. The noise reduction has been performed by the new proposed singular value decomposition based rank estimation method.Another classification has been realized by analyzing time-frequency characteristics of the signals. The time-frequency distribution has been investigated by wavelet transform since it supplies flexible time-frequency window. Classification in wavelet domain has been performed by wavelet entropy which is expressed by the sum of relative wavelet energies specified in certain frequency bands. Another wavelet based classification has been done by using the wavelet ridges where the energy is relatively maximum in time-frequency domain. These new proposed analysis methods have been applied to electrical signals taken from healthy human brains and the results have been compared with other studies.
Semiconductor Lasers
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Author : Junji Ohtsubo
language : en
Publisher: Springer
Release Date : 2012-10-05
Semiconductor Lasers written by Junji Ohtsubo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-05 with Science categories.
This third edition of “Semiconductor Lasers, Stability, Instability and Chaos” was significantly extended. In the previous edition, the dynamics and characteristics of chaos in semiconductor lasers after the introduction of the fundamental theory of laser chaos and chaotic dynamics induced by self-optical feedback and optical injection was discussed. Semiconductor lasers with new device structures, such as vertical-cavity surface-emitting lasers and broad-area semiconductor lasers, are interesting devices from the viewpoint of chaotic dynamics since they essentially involve chaotic dynamics even in their free-running oscillations. These topics are also treated with respect to the new developments in the current edition. Also the control of such instabilities and chaos control are critical issues for applications. Another interesting and important issue of semiconductor laser chaos in this third edition is chaos synchronization between two lasers and the application to optical secure communication. One of the new topics in this edition is fast physical number generation using chaotic semiconductor lasers for secure communication and development of chaos chips and their application. As other new important topics, the recent advance of new semiconductor laser structures is presented, such as quantum-dot semiconductor lasers, quantum-cascade semiconductor lasers, vertical-cavity surface-emitting lasers and physical random number generation with application to quantum key distribution. Stabilities, instabilities, and control of quantum-dot semiconductor lasers and quantum-cascade lasers are important topics in this field.
Practical Environmental Statistics And Data Analysis
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Author : Yue Rong
language : en
Publisher: ILM Publications
Release Date : 2011
Practical Environmental Statistics And Data Analysis written by Yue Rong and has been published by ILM Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
"Describes the application of statistical methods in different environmental fields, with an emphasis on how to solve real-world problems in complex systems"--Provided by publisher.
Nonlinear Dynamics And Time Series
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Author : Colleen D. Cutler
language : en
Publisher: American Mathematical Soc.
Release Date :
Nonlinear Dynamics And Time Series written by Colleen D. Cutler and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
Lars Ahlfors's Lectures on Quasiconformal Mappings, based on a course he gave at Harvard University in the spring term of 1964, was first published in 1966 and was soon recognized as the classic it was shortly destined to become. These lectures develop the theory of quasiconformal mappings from scratch, give a self-contained treatment of the Beltrami equation, and cover the basic properties of Teichmuller spaces, including the Bers embedding and the Teichmuller curve. It isremarkable how Ahlfors goes straight to the heart of the matter, presenting major results with a minimum set of prerequisites. Many graduate students and other mathematicians have learned the foundations of the theories of quasiconformal mappings and Teichmuller spaces from these lecture notes. This editionincludes three new chapters. The first, written by Earle and Kra, describes further developments in the theory of Teichmuller spaces and provides many references to the vast literature on Teichmuller spaces and quasiconformal mappings. The second, by Shishikura, describes how quasiconformal mappings have revitalized the subject of complex dynamics. The third, by Hubbard, illustrates the role of these mappings in Thurston's theory of hyperbolic structures on 3-manifolds. Together, these threenew chapters exhibit the continuing vitality and importance of the theory of quasiconformal mappings. This book is a collection of research and expository papers reflecting the interfacing of two fields: nonlinear dynamics (in the physiological and biological sciences) and statistics. It presents theproceedings of a four-day workshop entitled ''Nonlinear Dynamics and Time Series: Building a Bridge Between the Natural and Statistical Sciences'' held at the Centre de Recherches Mathematiques (CRM) in Montreal in July 1995. The goal of the workshop was to provide an exchange forum and to create a link between two diverse groups with a common interest in the analysis of nonlinear time series data. The editors and peer reviewers of this work have attempted to minimize the problems ofmaintaining communication between the different scientific fields. The result is a collection of interrelated papers that highlight current areas of research in statistics that might have particular applicability to nonlinear dynamics and new methodology and open data analysis problems in nonlinear dynamicsthat might find their way into the toolkits and research interests of statisticians. Features: A survey of state-of-the-art developments in nonlinear dynamics time series analysis with open statistical problems and areas for further research. Contributions by statisticians to understanding and improving modern techniques commonly associated with nonlinear time series analysis, such as surrogate data methods and estimation of local Lyapunov exponents. Starting point for both scientists andstatisticians who want to explore the field. Expositions that are readable to scientists outside the featured fields of specialization. Information for our distributors: Titles in this series are copublished with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario,Canada).
Chaos Detection And Predictability
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Author : Charalampos (Haris) Skokos
language : en
Publisher: Springer
Release Date : 2016-03-04
Chaos Detection And Predictability written by Charalampos (Haris) Skokos and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-04 with Science categories.
Distinguishing chaoticity from regularity in deterministic dynamical systems and specifying the subspace of the phase space in which instabilities are expected to occur is of utmost importance in as disparate areas as astronomy, particle physics and climate dynamics. To address these issues there exists a plethora of methods for chaos detection and predictability. The most commonly employed technique for investigating chaotic dynamics, i.e. the computation of Lyapunov exponents, however, may suffer a number of problems and drawbacks, for example when applied to noisy experimental data. In the last two decades, several novel methods have been developed for the fast and reliable determination of the regular or chaotic nature of orbits, aimed at overcoming the shortcomings of more traditional techniques. This set of lecture notes and tutorial reviews serves as an introduction to and overview of modern chaos detection and predictability techniques for graduate students and non-specialists. The book covers theoretical and computational aspects of traditional methods to calculate Lyapunov exponents, as well as of modern techniques like the Fast (FLI), the Orthogonal (OFLI) and the Relative (RLI) Lyapunov Indicators, the Mean Exponential Growth factor of Nearby Orbits (MEGNO), the Smaller (SALI) and the Generalized (GALI) Alignment Index and the ‘0-1’ test for chaos.
Chaos And Nonlinear Dynamics
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Author : Robert C. Hilborn
language : en
Publisher:
Release Date : 2000
Chaos And Nonlinear Dynamics written by Robert C. Hilborn and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This book introduces readers to the full range of current and background activity in the rapidly growing field of nonlinear dynamics. It uses a step-by-step introduction to dynamics and geometry in state space to help in understanding nonlinear dynamics and includes a thorough treatment of both differential equation models and iterated map models as well as a derivation of the famous Feigenbaum numbers. It is the only introductory book available that includes the important field of pattern formation and a survey of the controversial questions of quantum chaos. This second edition has been restructured for easier use and the extensive annotated references are updated through January 2000 and include many web sites for a number of the major nonlinear dynamics research centers. With over 200 figures and diagrams, analytic and computer exercises this book is a necessity for both the classroom and the lab.
Chaos In Hydrology
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Author : Bellie Sivakumar
language : en
Publisher: Springer
Release Date : 2016-11-16
Chaos In Hydrology written by Bellie Sivakumar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-16 with Science categories.
This authoritative book presents a comprehensive account of the essential roles of nonlinear dynamic and chaos theories in understanding, modeling, and forecasting hydrologic systems. This is done through a systematic presentation of: (1) information on the salient characteristics of hydrologic systems and on the existing theories for their modeling; (2) the fundamentals of nonlinear dynamic and chaos theories, methods for chaos identification and prediction, and associated issues; (3) a review of the applications of chaos theory in hydrology; and (4) the scope and potential directions for the future. This book bridges the divide between the deterministic and the stochastic schools in hydrology, and is well suited as a textbook for hydrology courses.
Chaos And Nonlinear Psychology
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Author : Ruth Richards
language : en
Publisher: Oxford University Press
Release Date : 2022
Chaos And Nonlinear Psychology written by Ruth Richards and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with Mathematics categories.
"Have you ever felt that human psychology is richer and more complex than the topics you learned in Psych 101, that great literature captured human motivational complexity better than scientists? Perhaps you, like the authors of this book, find that the linear math and statistical models that researchers have been using to capture psychology obscured many of the problems you would like to solve"--
Scientific Computing And Applications
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Author : Peter Minev
language : en
Publisher: Nova Publishers
Release Date : 2001
Scientific Computing And Applications written by Peter Minev and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Computers categories.
Scientific Computing & Applications