Chaos Detection And Predictability

Author : Charalampos (Haris) Skokos
Publisher : Springer
ISBN 13 : 3662484102
Total Pages : 269 pages
Book Rating : 4.04/5 ( download)

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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 269 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.

Author : Juan C. Vallejo
Publisher : Springer
ISBN 13 : 3319518933
Total Pages : 136 pages
Book Rating : 4.30/5 ( download)

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Download or read book Predictability of Chaotic Dynamics written by Juan C. Vallejo and published by Springer. This book was released on 2017-03-27 with total page 136 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 observation, modeling and computation are strongly interdependent. Unlike with physical systems under control in laboratories, for instance in celestial mechanics, one is confronted with the observation and modeling of systems without the possibility of altering the key parameters of the objects studied. Therefore, the numerical simulations offer an essential tool for analyzing these systems. With the widespread use of computer simulations to solve complex dynamical systems, the reliability of the numerical calculations is of ever-increasing interest and importance. This reliability is directly related to the regularity and instability properties of the modeled flow. 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 finite-time Lyapunov exponents approach. The method is illustrated using a number of well-known continuous dynamical systems, including the Contopoulos, Hénon-Heiles and Rössler systems. To help students and newcomers quickly learn to apply these techniques, the appendix provides descriptions of the algorithms used throughout the text and details how to implement them in order to solve a given continuous dynamical system.

Author : Adel Ouannas
Publisher : World Scientific
ISBN 13 : 9811271224
Total Pages : 218 pages
Book Rating : 4.29/5 ( download)

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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:

Author : Marius-F. Danca
Publisher : MDPI
ISBN 13 : 3036500928
Total Pages : 108 pages
Book Rating : 4.28/5 ( download)

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Download or read book Bifurcation and Chaos in Fractional-Order Systems written by Marius-F. Danca and published by MDPI. This book was released on 2021-01-19 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Paul Bracken
Publisher : BoD – Books on Demand
ISBN 13 : 1839628588
Total Pages : 265 pages
Book Rating : 4.80/5 ( download)

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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.

Author : George Datseris
Publisher : Springer Nature
ISBN 13 : 3030910326
Total Pages : 243 pages
Book Rating : 4.27/5 ( download)

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Download or read book Nonlinear Dynamics written by George Datseris and published by Springer Nature. This book was released on 2022-03-13 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Leonard Smith
Publisher : Oxford University Press
ISBN 13 : 0192853783
Total Pages : 201 pages
Book Rating : 4.83/5 ( download)

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Download or read book Chaos written by Leonard Smith and published by Oxford University Press. This book was released on 2007-02-22 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to chaotic behavior dynamics describes its behavior in both science and the real world.

Author : Stavros G. Stavrinides
Publisher : Springer Nature
ISBN 13 : 3030354415
Total Pages : 169 pages
Book Rating : 4.11/5 ( download)

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Download or read book Chaos and Complex Systems written by Stavros G. Stavrinides and published by Springer Nature. This book was released on 2020-02-19 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings of the “5th International Interdisciplinary Chaos Symposium on Chaos and Complex Systems (CCS).” All Symposia in the series bring together scientists, engineers, economists and social scientists, creating a vivid forum for discussions on the latest insights and findings obtained in the areas of complexity, nonlinear dynamics and chaos theory, as well as their interdisciplinary applications. The scope of the latest Symposium was enriched with a variety of contemporary, interdisciplinary topics, including but not limited to: fundamental theory of nonlinear dynamics, networks, circuits, systems, biology, evolution and ecology, fractals and pattern formation, nonlinear time series analysis, neural networks, sociophysics and econophysics, complexity management and global systems.

Author : Khalid M. Hosny
Publisher : Springer Nature
ISBN 13 : 3030387003
Total Pages : 271 pages
Book Rating : 4.06/5 ( download)

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Download or read book Multimedia Security Using Chaotic Maps: Principles and Methodologies written by Khalid M. Hosny and published by Springer Nature. This book was released on 2020-02-28 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive book is primarily intended for researchers, engineers, mathematicians and computer security specialists who are interested in multimedia security, steganography, encryption, and related research fields. It is also a valuable reference resource for postgraduate and senior undergraduate students who are studying multimedia, multimedia security, and information security, as well as for professionals in the IT industry.

Author : Kai-Uwe Sattler
Publisher : Springer Nature
ISBN 13 : 3030647196
Total Pages : 899 pages
Book Rating : 4.93/5 ( download)

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Download or read book Advances in Engineering Research and Application written by Kai-Uwe Sattler and published by Springer Nature. This book was released on 2020-11-23 with total page 899 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings book features volumes gathered selected contributions from the International Conference on Engineering Research and Applications (ICERA 2020) organized at Thai Nguyen University of Technology on December 1–2, 2020. The conference focused on the original researches in a broad range of areas, such as Mechanical Engineering, Materials and Mechanics of Materials, Mechatronics and Micromechatronics, Automotive Engineering, Electrical and Electronics Engineering, and Information and Communication Technology. Therefore, the book provides the research community with authoritative reports on developments in the most exciting areas in these fields.