Predictability Of Chaotic Dynamics
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Predictability Of Chaotic Dynamics
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Author : Juan C. Vallejo
language : en
Publisher: Springer Nature
Release Date : 2019-10-25
Predictability Of Chaotic Dynamics written by Juan C. Vallejo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-25 with Science categories.
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.
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.
Deep Learning In Multi Step Prediction Of Chaotic Dynamics
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Author : Matteo Sangiorgio
language : en
Publisher: Springer Nature
Release Date : 2022-02-14
Deep Learning In Multi Step Prediction Of Chaotic Dynamics written by Matteo Sangiorgio and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-14 with Mathematics categories.
The book represents the first attempt to systematically deal with the use of deep neural networks to forecast chaotic time series. Differently from most of the current literature, it implements a multi-step approach, i.e., the forecast of an entire interval of future values. This is relevant for many applications, such as model predictive control, that requires predicting the values for the whole receding horizon. Going progressively from deterministic models with different degrees of complexity and chaoticity to noisy systems and then to real-world cases, the book compares the performances of various neural network architectures (feed-forward and recurrent). It also introduces an innovative and powerful approach for training recurrent structures specific for sequence-to-sequence tasks. The book also presents one of the first attempts in the context of environmental time series forecasting of applying transfer-learning techniques such as domain adaptation.
Predictability Stability And Chaos In N Body Dynamical Systems
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Author : Archie E. Roy
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Predictability Stability And Chaos In N Body Dynamical Systems written by Archie E. Roy 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.
The reader will find in this volume the Proceedings of the NATO Advanced Study Institute held in Cortina d'Ampezzo, Italy between August 6 and August 17, 1990 under the title "Predictability, Stability, and Chaos in N-Body Dynamical Systems". The Institute was the latest in a series held at three-yearly inter vals from 1972 to 1987 in dynamical astronomy, theoretical mechanics and celestial mechanics. These previous institutes, held in high esteem by the international community of research workers, have resulted in a series of well-received Proceedings. The 1990 Institute attracted 74 participants from 16 countries, six outside the NATO group. Fifteen series of lectures were given by invited speakers; additionally some 40 valuable presentations were made by the younger participants, most of which are included in these Proceedings. The last twenty years in particular has been a time of increasingly rapid progress in tackling long-standing and also newly-arising problems in dynamics of N-body systems, point-mass and non-point-mass, a rate of progress achieved because of correspondingly rapid developments of new computer hardware and software together with the advent of new analytical techniques. It was a time of exciting progress culminating in the ability to carry out research programmes into the evolution of the outer Solar 8 System over periods of more than 10 years and to study star cluster and galactic models in unprecedented detail.
Chaotic Dynamics
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Author : Gregory L. Baker
language : en
Publisher: Cambridge University Press
Release Date : 1996
Chaotic Dynamics written by Gregory L. Baker and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Science categories.
The previous edition of this text was the first to provide a quantitative introduction to chaos and nonlinear dynamics at the undergraduate level. It was widely praised for the clarity of writing and for the unique and effective way in which the authors presented the basic ideas. These same qualities characterize this revised and expanded second edition. Interest in chaotic dynamics has grown explosively in recent years. Applications to practically every scientific field have had a far-reaching impact. As in the first edition, the authors present all the main features of chaotic dynamics using the damped, driven pendulum as the primary model. This second edition includes additional material on the analysis and characterization of chaotic data, and applications of chaos. This new edition of Chaotic Dynamics can be used as a text for courses on chaos for physics and engineering students at the second- and third-year level.
Chaos And Forecasting Proceedings Of The Royal Society Discussion Meeting
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Author : Howell A M Tong
language : en
Publisher: World Scientific
Release Date : 1995-04-26
Chaos And Forecasting Proceedings Of The Royal Society Discussion Meeting written by Howell A M Tong and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-04-26 with categories.
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.
Chaos
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Author : Angelo Vulpiani
language : en
Publisher: World Scientific
Release Date : 2010
Chaos written by Angelo Vulpiani and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
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.
Coping With Chaos
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Author : Edward Ott
language : en
Publisher: Wiley-VCH
Release Date : 1994-09-27
Coping With Chaos written by Edward Ott and has been published by Wiley-VCH this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-09-27 with Science categories.
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
Chaos
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Author : A.A. Tsonis
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Chaos written by A.A. Tsonis 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.
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.
Chaotic Dynamics
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Author : Tassos Bountis
language : en
Publisher: Springer Science & Business Media
Release Date : 1992
Chaotic Dynamics written by Tassos Bountis 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 1992 with Science categories.
These 37 papers are from the multidisciplinary NATO Advanced Study Institute on Chaotic Dynamics held in Patras, Greece, in July 1991. Among the diverse topics discussed were complexity, control and data representation; celestial mechanics and cosmology; controlling dynamical systems; semiconductors