Chaos Detection and Predictability - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Chaos Detection and Predictability write by Charalampos (Haris) Skokos. This book was released on 2016-03-04. Chaos Detection and Predictability available in PDF, EPUB and Kindle. 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.
Predictability of Chaotic Dynamics
Predictability of Chaotic Dynamics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Predictability of Chaotic Dynamics write by Juan C. Vallejo. This book was released on 2019-10-25. Predictability of Chaotic Dynamics available in PDF, EPUB and Kindle. 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 Methods and Predictability
Chaos Detection Methods and Predictability - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Chaos Detection Methods and Predictability write by . This book was released on 2014. Chaos Detection Methods and Predictability available in PDF, EPUB and Kindle.
Nonlinear Dynamics, Chaos, and Instability
Nonlinear Dynamics, Chaos, and Instability - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonlinear Dynamics, Chaos, and Instability write by William A. Brock. This book was released on 1991. Nonlinear Dynamics, Chaos, and Instability available in PDF, EPUB and Kindle. 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.
Fractional Discrete Chaos: Theories, Methods And Applications
Fractional Discrete Chaos: Theories, Methods And Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Fractional Discrete Chaos: Theories, Methods And Applications write by Adel Ouannas. This book was released on 2023-02-13. Fractional Discrete Chaos: Theories, Methods And Applications available in PDF, EPUB and Kindle. 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:
