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 Of Chaotic Dynamics
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Author : Juan C. Vallejo
language : es
Publisher:
Release Date : 2017
Predictability Of Chaotic Dynamics written by Juan C. Vallejo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with categories.
Predictability Of Complex Dynamical Systems
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Author : Yurii A. Kravtsov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Predictability Of Complex Dynamical Systems written by Yurii A. Kravtsov 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.
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".
Nonlinear Dynamics In Economics And Social Sciences
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Author : Franco Gori
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Dynamics In Economics And Social Sciences written by Franco Gori 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 Business & Economics categories.
This volume constitutes the Proceedings of the "Nonlinear Dynamics in Economics and Social Sciences" Meeting held at the Certosa di Pontignano, Siena, on May 27-30, 1991. The Meeting was organized by the National Group "Modelli Nonlineari in Economia e Dinamiche Complesse" of the Italian Ministery of University and SCientific Research, M.U.RS.T. The aim of the Conference, which followed a previous analogous initiative taking place in the very same Certosa, on January 1988*, was the one of offering a come together opportunity to economists interested in a new mathematical approach to the modelling of economical processes, through the use of more advanced analytical techniques, and mathematicians acting in the field of global dynamical systems theory and applications. A basiC underlying idea drove the organizers: the necessity of fOCUSing on the use that recent methods and results, as those commonly referred to the overpopularized label of "Chaotic Dynamics", did find in the social sciences domain; and thus to check their actual relevance in the research program of modelling economic phenomena, in order to individuate and stress promising perspectives, as well as to curb excessive hopes and criticize not infrequent cases where research reduces to mechanical, ad hoc, applications of "a la mode" techniques. In a word we felt the need of looking about the state of the arts in non-linear systems theory applications to economics and social processes: hence the title of the workshop and the volume.
Models And Applications Of Chaos Theory In Modern Sciences
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Author : Elhadj Zeraoulia
language : en
Publisher: CRC Press
Release Date : 2011-09-07
Models And Applications Of Chaos Theory In Modern Sciences written by Elhadj Zeraoulia and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-07 with Mathematics categories.
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
Nonlinear Dynamical Systems In Economics
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Author : Marji Lines
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-03-23
Nonlinear Dynamical Systems In Economics written by Marji Lines 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 2007-03-23 with Business & Economics categories.
Many problems in theoretical economics are mathematically formalized as dynam ical systems of difference and differential equations. In recent years a truly open approach to studying the dynamical behavior of these models has begun to make its way into the mainstream. That is, economists formulate their hypotheses and study the dynamics of the resulting models rather than formulating the dynamics and studying hypotheses that could lead to models with such dynamics. This is a great progress over using linear models, or using nonlinear models with a linear approach, or even squeezing economic models into well-studied nonlinear systems from other fields. There are today a number of economic journals open to publishing this type of work and some of these have become important. There are several societies which have annual meetings on the subject and participation at these has been growing at a good rate. And of course there are methods and techniques avail able to a more general audience, as well as a greater availability of software for numerical and graphical analysis that makes this type of research even more excit ing. The lecturers for the Advanced School on Nonlinear Dynamical Systems in Economics, who represent a wide selection of the research areas to which the the ory has been applied, agree on the importance of simulations and computer-based analysis. The School emphasized computer applications of models and methods, and all contributors ran computer lab sessions.
The Journal Of Agricultural Economics Research
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Author :
language : en
Publisher:
Release Date : 1991
The Journal Of Agricultural Economics Research written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Agriculture categories.
Oceanic And Atmospheric Fluid Dynamics
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Author : Stefano Pierini
language : en
Publisher: Springer Nature
Release Date : 2025-02-25
Oceanic And Atmospheric Fluid Dynamics written by Stefano Pierini and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-25 with Technology & Engineering categories.
This introductory text, based on the author's long-standing teaching experience, aims to provide a basic preparation of fluid dynamics, with particular attention to the dynamics of the oceans and the atmosphere, which require consideration of the Coriolis force. The most salient features of this text are its simplicity and compactness. As for simplicity, much attention has been paid to the connections between the various topics, not skimping on simple and intuitive explanations, so that the reader can easily acquire a unitary vision of the subject. As for its compactness, this is evident in the limited, yet sufficiently broad, range of topics analyzed, considered fundamental. This text is, therefore, particularly suitable for a wide audience of upper undergraduate students, but it also constitutes a valuable resource for master's and doctoral students, as well as to researchers who carry out their scientific activity in the broad context of meteorology, oceanography, and climatology.