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 Detection Methods and Predictability written by and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Predictability of Chaotic Dynamics written by Juan C. Vallejo and published by Springer Nature. This book was released on 2019-10-25 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is primarily concerned with the computational aspects of predictability of dynamical systems - in particular those where observations, modeling and computation are strongly interdependent. Unlike with physical systems under control in laboratories, in astronomy it is uncommon to have the possibility of altering the key parameters of the studied objects. Therefore, the numerical simulations offer an essential tool for analysing these systems, and their reliability is of ever-increasing interest and importance. In this interdisciplinary scenario, the underlying physics provide the simulated models, nonlinear dynamics provides their chaoticity and instability properties, and the computer sciences provide the actual numerical implementation. This book introduces and explores precisely this link between the models and their predictability characterization based on concepts derived from the field of nonlinear dynamics, with a focus on the strong sensitivity to initial conditions and the use of Lyapunov exponents to characterize this sensitivity. This method is illustrated using several well-known continuous dynamical systems, such as the Contopoulos, Hénon-Heiles and Rössler systems. This second edition revises and significantly enlarges the material of the first edition by providing new entry points for discussing new predictability issues on a variety of areas such as machine decision-making, partial differential equations or the analysis of attractors and basins. Finally, the parts of the book devoted to the application of these ideas to astronomy have been greatly enlarged, by first presenting some basics aspects of predictability in astronomy and then by expanding these ideas to a detailed analysis of a galactic potential.
Download or read book Chaos written by A.A. Tsonis and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on chaos theory two very important points are clear: (I) random looking aperiodic behavior may be the product of determinism, and (2) nonlinear problems should be treated as nonlinear problems and not as simplified linear problems. The theoretical aspects ofchaos have been presented in great detail in several excellent books published in the last five years or so. However, while the problems associated with applications of the theory-such as dimension and Lyapunov exponentsestimation, chaosand nonlinear pre diction, and noise reduction-have been discussed in workshops and ar ticles, they have not been presented in book form. This book has been prepared to fill this gap between theory and ap plicationsand to assist studentsand scientists wishingto apply ideas from the theory ofnonlinear dynamical systems to problems from their areas of interest. The book is intended to be used as a text for an upper-level undergraduate or graduate-level course, as well as a reference source for researchers. My philosophy behind writing this book was to keep it simple and informative without compromising accuracy. I have made an effort to presentthe conceptsby usingsimplesystemsand step-by-stepderivations. Anyone with an understanding ofbasic differential equations and matrix theory should follow the text without difficulty. The book was designed to be self-contained. When applicable, examples accompany the theory. The reader will notice, however, that in the later chapters specific examples become less frequent. This is purposely done in the hope that individuals will draw on their own ideas and research projects for examples.
Download or read book Chaos And Forecasting Proceedings Of The Royal Society Discussion Meeting written by Howell A M Tong and published by World Scientific. This book was released on 1995-04-26 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is now generally recognised that very simple dynamical systems can produce apparently random behaviour. In the last couple of years, attention has turned to focus on the flip side of this coin: random-looking time series (or random-looking patterns in space) may indeed be the result of very complicated processes or “real noise”, but they may equally well be produced by some very simple mechanism (a low-dimensional attractor). In either case, a long-term prediction will be possible only in probabilistic terms. However, in the very short term, random systems will still be unpredictable but low-dimensional chaotic ones may be predictable (appearances to the contrary). The Royal Society held a two-day discussion meeting on topics covering diverse fields, including biology, economics, geophysics, meteorology, statistics, epidemiology, earthquake science and many others. Each topic was covered by a leading expert in the field. The meeting dealt with different basic approaches to the problem of chaos and forecasting, and covered applications to nonlinear forecasting of both artificially-generated time series and real data from context in the above-mentioned diverse fields. This book marks a rather special and rare occasion on which prominent scientists from different areas converge on the same theme. It forms an informative introduction to the science of chaos, with special reference to real data.
Download or read book Chaos written by Angelo Vulpiani and published by World Scientific. This book was released on 2010 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaos: from simple models to complex systems aims to guide science and engineering students through chaos and nonlinear dynamics from classical examples to the most recent fields of research. The first part, intended for undergraduate and graduate students, is a gentle and self-contained introduction to the concepts and main tools for the characterization of deterministic chaotic systems, with emphasis to statistical approaches. The second part can be used as a reference by researchers as it focuses on more advanced topics including the characterization of chaos with tools of information theory and applications encompassing fluid and celestial mechanics, chemistry and biology. The book is novel in devoting attention to a few topics often overlooked in introductory textbooks and which are usually found only in advanced surveys such as: information and algorithmic complexity theory applied to chaos and generalization of Lyapunov exponents to account for spatiotemporal and non-infinitesimal perturbations. The selection of topics, numerous illustrations, exercises and proposals for computer experiments make the book ideal for both introductory and advanced courses. Sample Chapter(s). Introduction (164 KB). Chapter 1: First Encounter with Chaos (1,323 KB). Contents: First Encounter with Chaos; The Language of Dynamical Systems; Examples of Chaotic Behaviors; Probabilistic Approach to Chaos; Characterization of Chaotic Dynamical Systems; From Order to Chaos in Dissipative Systems; Chaos in Hamiltonian Systems; Chaos and Information Theory; Coarse-Grained Information and Large Scale Predictability; Chaos in Numerical and Laboratory Experiments; Chaos in Low Dimensional Systems; Spatiotemporal Chaos; Turbulence as a Dynamical System Problem; Chaos and Statistical Mechanics: Fermi-Pasta-Ulam a Case Study. Readership: Students and researchers in science (physics, chemistry, mathematics, biology) and engineering.
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 Fractional Discrete Chaos Theories Methods And Applications written by Adel Ouannas and published by World Scientific. This book was released on 2023-02-13 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the nineteenth-century, fractional calculus had its origin in extending differentiation and integration operators from the integer-order case to the fractional-order case. Discrete fractional calculus has recently become an important research topic, useful in various science and engineering applications. The first definition of the fractional-order discrete-time/difference operator was introduced in 1974 by Diaz and Osler, where such operator was derived by discretizing the fractional-order continuous-time operator. Successfully, several types of fractional-order difference operators have then been proposed and introduced through further generalizing numerous classical operators, motivating several researchers to publish extensively on a new class of systems, viz the nonlinear fractional-order discrete-time systems (or simply, the fractional-order maps), and their chaotic behaviors. This discovery of chaos in such maps, has led to novel control methods for effectively stabilizing their chaotic dynamics.The aims of this book are as follows:
Download or read book Nonlinear Dynamics Chaos and Instability written by William A. Brock and published by MIT Press. This book was released on 1991 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Brock, Hsieh, and LeBaron show how the principles of chaos theory can be applied to such areas of economics and finance as the changing structure of stock returns and nonlinearity in foreign exchange.
Download or read book A Collection of Papers on Chaos Theory and Its Applications written by Paul Bracken and published by BoD – Books on Demand. This book was released on 2021-04-14 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: This current volume contains 12 new papers on the subject of chaos in the physical sciences, which was initiated with the publication of the book Research Advances in Chaos Theory. It is clear the subject continues to attract a great deal of attention among scientists in the scientific community. This volume looks at such problems as chaos in nonlinear systems, in dynamical systems, quantum chaos, biological applications, and a few new emerging areas as well.
Download or read book Chaos Theory the Stock Market and Short Term Predictability written by Carl Andrew Taubel and published by . This book was released on 1993 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applications of Chaos and Nonlinear Dynamics in Science and Engineering Vol 2 written by Santo Banerjee and published by Springer. This book was released on 2012-07-17 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaos and nonlinear dynamics initially developed as a new emergent field with its foundation in physics and applied mathematics. The highly generic, interdisciplinary quality of the insights gained in the last few decades has spawned myriad applications in almost all branches of science and technology—and even well beyond. Wherever the quantitative modeling and analysis of complex, nonlinear phenomena are required, chaos theory and its methods can play a key role. This second volume concentrates on reviewing further relevant, contemporary applications of chaotic nonlinear systems as they apply to the various cutting-edge branches of engineering. This encompasses, but is not limited to, topics such as the spread of epidemics; electronic circuits; chaos control in mechanical devices; secure communication; and digital watermarking. Featuring contributions from active and leading research groups, this collection is ideal both as a reference work and as a ‘recipe book’ full of tried and tested, successful engineering applications.
Download or read book Models and Applications of Chaos Theory in Modern Sciences written by Elhadj Zeraoulia and published by CRC Press. This book was released on 2011-09-07 with total page 742 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a select group of papers that provide a comprehensive view of the models and applications of chaos theory in medicine, biology, ecology, economy, electronics, mechanical, and the human sciences. Covering both the experimental and theoretical aspects of the subject, it examines a range of current topics of interest. It consid
Download or read book Predictability of Complex Dynamical Systems written by Yurii A. Kravtsov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book book for researchers and practitioners interested in modeling, prediction and forecasting of natural systems based on nonlinear dynamics. It is a practical guide to data analysis and to the development of algorithms, especially for complex systems. Topics such as the characterization of nonlinear correlations in data as dynamical systems, reconstruction of dynamical models from data, nonlinear noise reduction and the limits of predicatability are discussed. The chapters are written by leading experts and consider practical problems such as signal and time series analysis, biomedical data analysis, financial analysis, stochastic modeling, human evolution, and political modeling. The book includes new methods for nonlinear filtering of complex signals, new algorithms for signal classification, and the concept of the "Global Brain".
Download or read book Beyond Belief written by John L. Casti and published by CRC Press. This book was released on 2018-02-06 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: How can we predict and explain the phenomena of nature? What are the limits to this knowledge process? The central issues of prediction, explanation, and mathematical modeling, which underlie all scientific activity, were the focus of a conference organized by the Swedish Council for the Planning and Coordination of Research, held at the Abisko Research Station in May of 1989. At this forum, a select group of internationally known scientists in physics, chemistry, biology, economics, sociology and mathematics discussed and debated the ways in which prediction and explanation interact with mathematical modeling in their respective areas of expertise. Beyond Belief is the result of this forum, consisting of 11 chapters written specifically for this volume. The multiple themes of randomness, uncertainty, prediction and explanation are presented using (as vehicles) several topical areas from modern science, such as morphogenetic fields, Boscovich covariance, and atmospheric variability. This multidisciplinary examination of the foundational issues of modern scientific thought and methodology will offer stimulating reading for a very broad scientific audience.
Download or read book Chaotic Signal Processing written by Henry Leung and published by SIAM. This book was released on 2013-12-05 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authoritative guide to up-to-date research results on chaotic signal processing aimed at researchers and graduate students in chaos, applied nonlinear dynamics, signal processing and radar communications. This book examines the applications of chaotic signal processing to radar, communications, system identification and computing.
Download or read book Characterization of Normality of Chaotic Systems Including Prediction and Detection of Anomalies written by Joseph John Engler and published by . This book was released on 2011 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: The dissertation addresses these goals by proposing new representational techniques and novel prediction methodologies. The value and efficiency of these methods are explored in various case studies. Presented is an overview of chaotic systems with examples taken from the real world. A representation schema for rapid understanding of the various states of deterministically chaotic systems is presented. This schema is then used to detect anomalies and system state changes. Additionally, a novel prediction methodology which utilizes Lyapunov exponents to facilitate longer term prediction accuracy is presented and compared with other nonlinear prediction methodologies. These novel methodologies are then demonstrated on applications such as wind energy, cyber security and classification of social networks.
