Download or read book Analysis of Observed Chaotic Data written by Henry Abarbanel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: A clear and systematic treatment of time series of data, regular and chaotic, found in nonlinear systems. The text leads readers 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. It 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 modern mathematical tools for investigating chaotic behaviour to uncover properties of physical systems, requiring knowledge of dynamical systems at the advanced undergraduate level and some knowledge of Fourier transforms and other signal processing methods.
Download or read book Analysis of Observed Chaotic Data written by Mehmet Emre Çek and published by . This book was released on 2004 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Measures of Complexity and Chaos written by Neal B. Abraham and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume serves as a general introduction to the state of the art of quantitatively characterizing chaotic and turbulent behavior. It is the outgrowth of an international workshop on "Quantitative Measures of Dynamical Complexity and Chaos" held at Bryn Mawr College, June 22-24, 1989. The workshop was co-sponsored by the Naval Air Development Center in Warminster, PA and by the NATO Scientific Affairs Programme through its special program on Chaos and Complexity. Meetings on this subject have occurred regularly since the NATO workshop held in June 1983 at Haverford College only two kilometers distant from the site of this latest in the series. At that first meeting, organized by J. Gollub and H. Swinney, quantitative tests for nonlinear dynamics and chaotic behavior were debated and promoted [1). In the six years since, the methods for dimension, entropy and Lyapunov exponent calculations have been applied in many disciplines and the procedures have been refined. Since then it has been necessary to demonstrate quantitatively that a signal is chaotic rather than it being acceptable to observe that "it looks chaotic". Other related meetings have included the Pecos River Ranch meeting in September 1985 of G. Mayer Kress [2) and the reflective and forward looking gathering near Jerusalem organized by M. Shapiro and I. Procaccia in December 1986 [3). This meeting was proof that interest in measuring chaotic and turbulent signals is widespread.
Download or read book Nonlinear Time Series Analysis written by Holger Kantz and published by Cambridge University Press. This book was released on 2004 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: The paradigm of deterministic chaos has influenced thinking in many fields of science. Chaotic systems show rich and surprising mathematical structures. In the applied sciences, deterministic chaos provides a striking explanation for irregular behaviour and anomalies in systems which do not seem to be inherently stochastic. The most direct link between chaos theory and the real world is the analysis of time series from real systems in terms of nonlinear dynamics. Experimental technique and data analysis have seen such dramatic progress that, by now, most fundamental properties of nonlinear dynamical systems have been observed in the laboratory. Great efforts are being made to exploit ideas from chaos theory wherever the data displays more structure than can be captured by traditional methods. Problems of this kind are typical in biology and physiology but also in geophysics, economics, and many other sciences.
Download or read book Modelling and Forecasting Financial Data written by Abdol S. Soofi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modelling and Forecasting Financial Data brings together a coherent and accessible set of chapters on recent research results on this topic. To make such methods readily useful in practice, the contributors to this volume have agreed to make available to readers upon request all computer programs used to implement the methods discussed in their respective chapters. Modelling and Forecasting Financial Data is a valuable resource for researchers and graduate students studying complex systems in finance, biology, and physics, as well as those applying such methods to nonlinear time series analysis and signal processing.
Download or read book Handbook of Applications of Chaos Theory written by Christos H. Skiadas and published by CRC Press. This book was released on 2017-12-19 with total page 921 pages. Available in PDF, EPUB and Kindle. Book excerpt: In addition to explaining and modeling unexplored phenomena in nature and society, chaos uses vital parts of nonlinear dynamical systems theory and established chaotic theory to open new frontiers and fields of study. Handbook of Applications of Chaos Theory covers the main parts of chaos theory along with various applications to diverse areas. Expert contributors from around the world show how chaos theory is used to model unexplored cases and stimulate new applications. Accessible to scientists, engineers, and practitioners in a variety of fields, the book discusses the intermittency route to chaos, evolutionary dynamics and deterministic chaos, and the transition to phase synchronization chaos. It presents important contributions on strange attractors, self-exciting and hidden attractors, stability theory, Lyapunov exponents, and chaotic analysis. It explores the state of the art of chaos in plasma physics, plasma harmonics, and overtone coupling. It also describes flows and turbulence, chaotic interference versus decoherence, and an application of microwave networks to the simulation of quantum graphs. The book proceeds to give a detailed presentation of the chaotic, rogue, and noisy optical dissipative solitons; parhelic-like circle and chaotic light scattering; and interesting forms of the hyperbolic prism, the Poincaré disc, and foams. It also covers numerous application areas, from the analysis of blood pressure data and clinical digital pathology to chaotic pattern recognition to economics to musical arts and research.
Download or read book Chaos in Real Data written by J.N. Perry and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaos in Real Data studies the range of data analytic techniques available to study nonlinear population dynamics for ecological time series. Several case studies are studied using typically short and noisy population data from field and laboratory. A range of modern approaches, such as response surface methodology and mechanistic mathematical modelling, are applied to several case studies. Experts honestly appraise how well these methods have performed on their data. The accessible style of the book ensures its readability for non-quantitative biologists. The data remain available, as benchmarks for future study, on the worldwide web.
Download or read book Coping with Chaos written by Edward Ott and published by Wiley-VCH. This book was released on 1994-09-27 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first unified presentation of new developments in the analysis and exploitation of chaotic systems... Mathematicians have been aware of chaotic dynamics since Poincar?'s work at the turn of the century. But, as the turn of yet another century approaches, physical scientists and engineers have begun to use their understanding of chaos theory to analyze chaotic experimental time series data. Some researchers have even used the presence of chaos to achieve practical goals. To do this, they have had to work with dynamical processes for which the equations were either not known or were too complex to be useful. In other words, they have been coping with chaos. Coping with Chaos is the first book to bring together recent advances in the interpretive and practical applications of chaos, which hold great promise for broad applicability throughout the physical sciences and engineering. Together with an introduction to chaos theory, this book provides detailed reports on methods of analyzing experimental time series data from chaotic systems and studies in which the unique attributes of chaos are put to practical use. Topics discussed in this book include: * Theory of chaotic dynamics * Embedding techniques for the analysis of experimental data * Calculation of dimension and Lyapunov exponents * Determination of periodic orbits and symbolic dynamics * Prediction of chaotic time series * Noise filtering of chaotic data * Control of chaotic systems * The use of chaotic signals for communication * And more
Download or read book Nonlinear Analysis of Physiological Data written by Holger Kantz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is more than a standard proceedings volume, although it is an almost direct result of the workshop on "Nonlinear Analysis of Physiologi cal Time Series" held in Freital near Dresden, Germany, in October 1995. The idea of the meeting was, as for previous meetings devoted to related topics, such as the conference on dynamical diseases held near Montreal in February 1994 (see CHAOS Vol. 5(1), 1995), to bring together experts on the techniques of nonlinear analysis and the theory of chaos and applicants from the most fascinating field where such methods could potentially be useful: the life sciences. The former group consisted mainly of physicists and mathe maticians, the latter was represented by physiologists and medical researchers and practitioners. Many aspects of this workshop were unusual and not previously expe rienced. Also, the hosting institution, the Max Planck Institute for Physics of Complex Systems (MPIPKS), at this time was brand new. The organiz ers' rather unconventional intention was to bring specialists of both groups together to really work together. Therefore, there was an excessive availabil ity of computers and the possibility to numerically study time series data sets practitioners had supplied from their own fields, e. g. electrocardiogram (ECG) data, electroencephalogram (EEG) data, data from the respiratory system, from human voice, human posture control, and several others. These data formed a much stronger link between theoreticians and applicants than any of the common ideas.
Download or read book Controlling Chaos and Bifurcations in Engineering Systems written by Guanrong Chen and published by CRC Press. This book was released on 1999-09-28 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last two decades, chaos in engineering systems has moved from being simply a curious phenomenon to one with real, practical significance and utility. Engineers, scientists, and mathematicians have similarly advanced from the passive role of analyzing chaos to their present, active role of controlling chaos-control directed not only at suppression, but also at exploiting its enormous potential. We now stand at the threshold of major advances in the control and synchronization of chaos for new applications across the range of engineering disciplines. Controlling Chaos and Bifurcations in Engineering Systems provides a state-of-the-art survey of the control-and anti-control-of chaos in dynamical systems. Internationally known experts in the field join forces in this volume to form this tutorial-style combination of overview and technical report on the latest advances in the theory and applications of chaos control. They detail various approaches to control and show how designers can use chaos to create a wider variety of properties and greater flexibility in the design process. Chaos control promises to have a major impact on novel time- and energy-critical engineering applications. Within this volume, readers will find many challenging problems-yet unsolved-regarding both the fundamental theory and potential applications of chaos control and anti-control. Controlling Chaos and Bifurcations in Engineering Systems will bring readers up-to-date on recent development in the field and help open the door to new advances.
Download or read book Semiconductor Lasers written by Junji Ohtsubo and published by Springer. This book was released on 2012-10-05 with total page 579 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Practical Environmental Statistics and Data Analysis written by Yue Rong and published by ILM Publications. This book was released on 2011 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.
Download or read book Nonlinear Dynamics and Time Series written by Colleen D. Cutler and published by American Mathematical Soc.. This book was released on with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Download or read book Chaos Detection and Predictability written by Charalampos (Haris) Skokos and published by Springer. This book was released on 2016-03-04 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Chaos and Nonlinear Dynamics written by Robert C. Hilborn and published by . This book was released on 2000 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Statistical Physics of Data Assimilation and Machine Learning written by Henry D. I. Abarbanel and published by Cambridge University Press. This book was released on 2022-02-17 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of data assimilation and machine learning is introduced in an accessible manner for undergraduate and graduate students.
Download or read book Chaos A Statistical Perspective written by Kung-Sik Chan and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses dynamical systems that are typically driven by stochastic dynamic noise. It is written by two statisticians essentially for the statistically inclined readers. It covers many of the contributions made by the statisticians in the past twenty years or so towards our understanding of estimation, the Lyapunov-like index, the nonparametric regression, and many others, many of which are motivated by their dynamical system counterparts but have now acquired a distinct statistical flavor.
