Chaos Detection And Predictability
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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 Detection Methods And Predictability
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Author :
language : en
Publisher:
Release Date : 2014
Chaos Detection Methods And Predictability written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.
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.
Fractional Discrete Chaos Theories Methods And Applications
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Author : Adel Ouannas
language : en
Publisher: World Scientific
Release Date : 2023-02-13
Fractional Discrete Chaos Theories Methods And Applications written by Adel Ouannas and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-13 with Science categories.
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:
Data Science
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Author : Robert Stahlbock
language : en
Publisher: Springer Nature
Release Date : 2025-04-16
Data Science written by Robert Stahlbock and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-16 with Computers categories.
This book constitutes the proceedings of the 20th International Conference on Data Science, ICDATA 2024, held as part of the 2024 World Congress in Computer Science, Computer Engineering and Applied Computing, in Las Vegas, USA, during July 22 to July 25, 2024. This proceedings book includes 39 papers selected from a total of 243 submissions. They are organized in topical sections as follows: Artificial intelligence, data science, and neural networks; natural language processing, large language modelc, generative AI; data science, data analytics, and applications; prediction and forecasting and security applications; and poster papers.
Nonlinear Systems And Matrix Analysis Recent Advances In Theory And Applications
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Author : Peter Chen
language : en
Publisher: BoD – Books on Demand
Release Date : 2024-11-27
Nonlinear Systems And Matrix Analysis Recent Advances In Theory And Applications written by Peter Chen and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-27 with Mathematics categories.
Nonlinear system analysis is of interest to engineers, sociologists, physicists, mathematicians, and many other scientists since most systems are inherently nonlinear in nature. In mathematics, a nonlinear system does not satisfy the superposition principle such as in a linear system. Therefore, the theories underlining nonlinear analysis and their applications need to be developed on their own merit. The first section of this book is a collection of examples reporting recent advances in both theory and applications of nonlinear system analysis. The contents of each chapter will provide in-depth foresight to interested readers. As numerical linearization to a set of matrix equations is still the principal method used to solve a nonlinear system, matrix analysis is the topic of the second section of this book. The matrices have invaded practically all areas of mathematics, the experimental and social sciences, engineering, and technology. This volume updates purely mathematical theoretical aspects, and it also presents concrete examples of the wide range of applications of matrix theory in other disciplines.
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.
Bifurcation And Chaos In Fractional Order Systems
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Author : Marius-F. Danca
language : en
Publisher: MDPI
Release Date : 2021-01-19
Bifurcation And Chaos In Fractional Order Systems written by Marius-F. Danca and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-19 with Technology & Engineering categories.
This book presents a collection of seven technical papers on fractional-order complex systems, especially chaotic systems with hidden attractors and symmetries, in the research front of the field, which will be beneficial for scientific researchers, graduate students, and technical professionals to study and apply. It is also suitable for teaching lectures and for seminars to use as a reference on related topics.
Nonlinear Dynamics
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Author : George Datseris
language : en
Publisher: Springer Nature
Release Date : 2022-03-13
Nonlinear Dynamics written by George Datseris and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-13 with Science categories.
This concise and up-to-date textbook provides an accessible introduction to the core concepts of nonlinear dynamics as well as its existing and potential applications. The book is aimed at students and researchers in all the diverse fields in which nonlinear phenomena are important. Since most tasks in nonlinear dynamics cannot be treated analytically, skills in using numerical simulations are crucial for analyzing these phenomena. The text therefore addresses in detail appropriate computational methods as well as identifying the pitfalls of numerical simulations. It includes numerous executable code snippets referring to open source Julia software packages. Each chapter includes a selection of exercises with which students can test and deepen their skills.
Managing In Uncertainty Theory And Practice
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Author : Constantin Zopounidis
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Managing In Uncertainty Theory And Practice written by Constantin Zopounidis 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 2013-04-17 with Business & Economics categories.
This book provides a new point of view on the subject of the management of uncertainty. It covers a wide variety of both theoretical and practical issues involving the analysis and management of uncertainty in the fields of finance, management and marketing. Audience: Researchers and professionals from operations research, management science and economics.