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Attractor Dimension Estimates For Dynamical Systems Theory And Computation
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Book Synopsis Attractor Dimension Estimates for Dynamical Systems: Theory and Computation by : Nikolay Kuznetsov
Download or read book Attractor Dimension Estimates for Dynamical Systems: Theory and Computation written by Nikolay Kuznetsov and published by Springer Nature. This book was released on 2020-07-02 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides analytical and numerical methods for the estimation of dimension characteristics (Hausdorff, Fractal, Carathéodory dimensions) for attractors and invariant sets of dynamical systems and cocycles generated by smooth differential equations or maps in finite-dimensional Euclidean spaces or on manifolds. It also discusses stability investigations using estimates based on Lyapunov functions and adapted metrics. Moreover, it introduces various types of Lyapunov dimensions of dynamical systems with respect to an invariant set, based on local, global and uniform Lyapunov exponents, and derives analytical formulas for the Lyapunov dimension of the attractors of the Hénon and Lorenz systems. Lastly, the book presents estimates of the topological entropy for general dynamical systems in metric spaces and estimates of the topological dimension for orbit closures of almost periodic solutions to differential equations.
Book Synopsis Chaotic Systems with Multistability and Hidden Attractors by : Xiong Wang
Download or read book Chaotic Systems with Multistability and Hidden Attractors written by Xiong Wang and published by Springer Nature. This book was released on 2021-12-01 with total page 661 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a collection of new articles written by world-leading experts and active researchers to present their recent finding and progress in the new area of chaotic systems and dynamics, regarding emerging subjects of unconventional chaotic systems and their complex dynamics.It guide readers directly to the research front of the new scientific studies. This book is unique of its kind in the current literature, presenting broad scientific research topics including multistability and hidden attractors in unconventional chaotic systems, such as chaotic systems without equilibria, with only stable equilibria, with a curve or a surface of equilibria. The book describes many novel phenomena observed from chaotic systems, such as non-Shilnikov type chaos, coexistence of different types of attractors, and spontaneous symmetry breaking in chaotic systems. The book presents state-of-the-art scientific research progress in the field with both theoretical advances and potential applications. This book is suitable for all researchers and professionals in the areas of nonlinear dynamics and complex systems, including research professionals, physicists, applied mathematicians, computer scientists and, in particular, graduate students in related fields.
Book Synopsis Artificial Intelligence Applications and Innovations by : Ilias Maglogiannis
Download or read book Artificial Intelligence Applications and Innovations written by Ilias Maglogiannis and published by Springer Nature. This book was released on 2021-06-22 with total page 801 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 17th IFIP WG 12.5 International Conference on Artificial Intelligence Applications and Innovations, AIAI 2021, held virtually and in Hersonissos, Crete, Greece, in June 2021. The 50 full papers and 11 short papers presented were carefully reviewed and selected from 113 submissions. They cover a broad range of topics related to technical, legal, and ethical aspects of artificial intelligence systems and their applications and are organized in the following sections: adaptive modeling/ neuroscience; AI in biomedical applications; AI impacts/ big data; automated machine learning; autonomous agents; clustering; convolutional NN; data mining/ word counts; deep learning; fuzzy modeling; hyperdimensional computing; Internet of Things/ Internet of energy; machine learning; multi-agent systems; natural language; recommendation systems; sentiment analysis; and smart blockchain applications/ cybersecurity. Chapter “Improving the Flexibility of Production Scheduling in Flat Steel Production Through Standard and AI-based Approaches: Challenges and Perspective” is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
Book Synopsis Attractors and Methods by : Boling Guo
Download or read book Attractors and Methods written by Boling Guo and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-07-09 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume work presents state-of-the-art mathematical theories and results on infinite-dimensional dynamical systems. Inertial manifolds, approximate inertial manifolds, discrete attractors and the dynamics of small dissipation are discussed in detail. The unique combination of mathematical rigor and physical background makes this work an essential reference for researchers and graduate students in applied mathematics and physics. The main emphasis in the fi rst volume is on the existence and properties for attractors and inertial manifolds. This volume highlights the use of modern analytical tools and methods such as the geometric measure method, center manifold theory in infinite dimensions, the Melnihov method, spectral analysis and so on for infinite-dimensional dynamical systems. The second volume includes the properties of global attractors, the calculation of discrete attractors, structures of small dissipative dynamical systems, and the existence and stability of solitary waves. Contents Discrete attractor and approximate calculation Some properties of global attractor Structures of small dissipative dynamical systems Existence and stability of solitary waves
Book Synopsis Handbook of Dynamical Systems by : B. Fiedler
Download or read book Handbook of Dynamical Systems written by B. Fiedler and published by Gulf Professional Publishing. This book was released on 2002-02-21 with total page 1099 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook is volume II in a series collecting mathematical state-of-the-art surveys in the field of dynamical systems. Much of this field has developed from interactions with other areas of science, and this volume shows how concepts of dynamical systems further the understanding of mathematical issues that arise in applications. Although modeling issues are addressed, the central theme is the mathematically rigorous investigation of the resulting differential equations and their dynamic behavior. However, the authors and editors have made an effort to ensure readability on a non-technical level for mathematicians from other fields and for other scientists and engineers. The eighteen surveys collected here do not aspire to encyclopedic completeness, but present selected paradigms. The surveys are grouped into those emphasizing finite-dimensional methods, numerics, topological methods, and partial differential equations. Application areas include the dynamics of neural networks, fluid flows, nonlinear optics, and many others.While the survey articles can be read independently, they deeply share recurrent themes from dynamical systems. Attractors, bifurcations, center manifolds, dimension reduction, ergodicity, homoclinicity, hyperbolicity, invariant and inertial manifolds, normal forms, recurrence, shift dynamics, stability, to namejust a few, are ubiquitous dynamical concepts throughout the articles.
Author :Carlos Castillo-Chavez Publisher :Springer Science & Business Media ISBN 13 :3642466931 Total Pages :340 pages Book Rating :4.6/5 (424 download)
Book Synopsis Mathematical Approaches to Problems in Resource Management and Epidemiology by : Carlos Castillo-Chavez
Download or read book Mathematical Approaches to Problems in Resource Management and Epidemiology written by Carlos Castillo-Chavez and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Increasingly, mathematical methods are being used to advantage in addressing the problems facing humanity in managing its environment. Problems in resource management and epidemiology especially have demonstrated the utility of quantitative modeling. To explore these approaches, the Center of Applied Mathematics at Cornell University organized a conference in Fall, 1987, with the objective of surveying and assessing the state of the art. This volume records the proceedings of that conference. Underlying virtually all of these studies are models of population growth, from individual cells to large vertebrates. Cell population growth presents the simplest of systems for study, and is of fundamental importance in its own right for a variety of medical and environmental applications. In Part I of this volume, Michael Shuler describes computer models of individual cells and cell populations, and Frank Hoppensteadt discusses the synchronization of bacterial culture growth. Together, these provide a valuable introduction to mathematical cell biology.
Book Synopsis From Topology to Computation: Proceedings of the Smalefest by : Morris W. Hirsch
Download or read book From Topology to Computation: Proceedings of the Smalefest written by Morris W. Hirsch and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: An extraordinary mathematical conference was held 5-9 August 1990 at the University of California at Berkeley: From Topology to Computation: Unity and Diversity in the Mathematical Sciences An International Research Conference in Honor of Stephen Smale's 60th Birthday The topics of the conference were some of the fields in which Smale has worked: • Differential Topology • Mathematical Economics • Dynamical Systems • Theory of Computation • Nonlinear Functional Analysis • Physical and Biological Applications This book comprises the proceedings of that conference. The goal of the conference was to gather in a single meeting mathemati cians working in the many fields to which Smale has made lasting con tributions. The theme "Unity and Diversity" is enlarged upon in the section entitled "Research Themes and Conference Schedule." The organizers hoped that illuminating connections between seemingly separate mathematical sub jects would emerge from the conference. Since such connections are not easily made in formal mathematical papers, the conference included discussions after each of the historical reviews of Smale's work in different fields. In addition, there was a final panel discussion at the end of the conference.
Author :Sergey N. Vladimirov Publisher :Scientific Research Publishing, Inc. USA ISBN 13 :1618960563 Total Pages :240 pages Book Rating :4.6/5 (189 download)
Book Synopsis Non-traditional Dynamics in Electronics: Theory and Practice by : Sergey N. Vladimirov
Download or read book Non-traditional Dynamics in Electronics: Theory and Practice written by Sergey N. Vladimirov and published by Scientific Research Publishing, Inc. USA. This book was released on 2010-10-04 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main theme of the proposed book is devoted to investigation of non-trivial problems of functioning of Ultra-High-Frequency (UHF) electronic devices and systems in the various type dynamic instability modes. Both flows and maps (representations) are considered because the relation between maps and flows was repeatedly discussed in different publications. On the contrary, all systems described in the offered book for the first time are considered from the point of view either internal structure, or the description and analysis.
Author :Gottfried Mayer-Kress Publisher :Springer Science & Business Media ISBN 13 :3642710018 Total Pages :264 pages Book Rating :4.6/5 (427 download)
Book Synopsis Dimensions and Entropies in Chaotic Systems by : Gottfried Mayer-Kress
Download or read book Dimensions and Entropies in Chaotic Systems written by Gottfried Mayer-Kress and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings contain the papers contributed to the International Work shop on "Dimensions and Entropies in Chaotic Systems" at the Pecos River Conference Center on the Pecos River Ranch in Spetember 1985. The work shop was held by the Center for Nonlinear Studies of the Los Alamos National Laboratory. At the Center for Nonlinear Studies the investigation of chaotic dynamics and especially the quantification of complex behavior has a long tradition. In spite of some remarkable successes, there are fundamental, as well as nu merical, problems involved in the practical realization of these algorithms. This has led to a series of publications in which modifications and improve ments of the original methods have been proposed. At present there exists a growing number of competing dimension algorithms but no comprehensive review explaining how they are related. Further, in actual experimental ap plications, rather than a precise algorithm, one finds frequent use of "rules of thumb" together with error estimates which, in many cases, appear to be far too optimistic. Also it seems that questions like "What is the maximal dimension of an attractor that one can measure with a given number of data points and a given experimental resolution?" have still not been answered in a satisfactory manner for general cases.
Book Synopsis Applied Analysis of the Navier-Stokes Equations by : Charles R. Doering
Download or read book Applied Analysis of the Navier-Stokes Equations written by Charles R. Doering and published by Cambridge University Press. This book was released on 1995 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory physical and mathematical presentation of the Navier-Stokes equations focuses on unresolved questions of the regularity of solutions in three spatial dimensions, and the relation of these issues to the physical phenomenon of turbulent fluid motion.
Book Synopsis Modern Mathematical Methods and High Performance Computing in Science and Technology by : Vinai K. Singh
Download or read book Modern Mathematical Methods and High Performance Computing in Science and Technology written by Vinai K. Singh and published by Springer. This book was released on 2016-08-06 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book discusses important results in modern mathematical models and high performance computing, such as applied operations research, simulation of operations, statistical modeling and applications, invisibility regions and regular meta-materials, unmanned vehicles, modern radar techniques/SAR imaging, satellite remote sensing, coding, and robotic systems. Furthermore, it is valuable as a reference work and as a basis for further study and research. All contributing authors are respected academicians, scientists and researchers from around the globe. All the papers were presented at the international conference on Modern Mathematical Methods and High Performance Computing in Science & Technology (M3HPCST 2015), held at Raj Kumar Goel Institute of Technology, Ghaziabad, India, from 27–29 December 2015, and peer-reviewed by international experts. The conference provided an exceptional platform for leading researchers, academicians, developers, engineers and technocrats from a broad range of disciplines to meet and discuss state-of-the-art mathematical methods and high performance computing in science & technology solutions. This has brought new prospects for collaboration across disciplines and ideas that facilitate novel breakthroughs.
Book Synopsis Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields by : John Guckenheimer
Download or read book Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields written by John Guckenheimer and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help readers develop an intuitive feel for the properties involved.
Book Synopsis Discrete and Continuous Dynamical Systems by :
Download or read book Discrete and Continuous Dynamical Systems written by and published by . This book was released on 2008 with total page 738 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Non-Linear Variability in Geophysics by : D. Schertzer
Download or read book Non-Linear Variability in Geophysics written by D. Schertzer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: consequences of broken symmetry -here parity-is studied. In this model, turbulence is dominated by a hierarchy of helical (corkscrew) structures. The authors stress the unique features of such pseudo-scalar cascades as well as the extreme nature of the resulting (intermittent) fluctuations. Intermittent turbulent cascades was also the theme of a paper by us in which we show that universality classes exist for continuous cascades (in which an infinite number of cascade steps occur over a finite range of scales). This result is the multiplicative analogue of the familiar central limit theorem for the addition of random variables. Finally, an interesting paper by Pasmanter investigates the scaling associated with anomolous diffusion in a chaotic tidal basin model involving a small number of degrees of freedom. Although the statistical literature is replete with techniques for dealing with those random processes characterized by both exponentially decaying (non-scaling) autocorrelations and exponentially decaying probability distributions, there is a real paucity of literature appropriate for geophysical fields exhibiting either scaling over wide ranges (e. g. algebraic autocorrelations) or extreme fluctuations (e. g. algebraic probabilities, divergence of high order statistical moments). In fact, about the only relevant technique that is regularly used -fourier analysis (energy spectra) -permits only an estimate of a single (power law) exponent. If the fields were mono-fractal (characterized by a single fractal dimension) this would be sufficient, however their generally multifractal character calls for the development of new techniques.
Book Synopsis Soft Computing and Fractal Theory for Intelligent Manufacturing by : Oscar Castillo
Download or read book Soft Computing and Fractal Theory for Intelligent Manufacturing written by Oscar Castillo and published by Physica. This book was released on 2012-08-11 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: We describe in this book, new methods for intelligent manufacturing using soft computing techniques and fractal theory. Soft Computing (SC) consists of several computing paradigms, including fuzzy logic, neural networks, and genetic algorithms, which can be used to produce powerful hybrid intelligent systems. Fractal theory provides us with the mathematical tools to understand the geometrical complexity of natural objects and can be used for identification and modeling purposes. Combining SC techniques with fractal theory, we can take advantage of the "intelligence" provided by the computer methods and also take advantage of the descriptive power of the fractal mathematical tools. Industrial manufacturing systems can be considered as non-linear dynamical systems, and as a consequence can have highly complex dynamic behaviors. For this reason, the need for computational intelligence in these manufacturing systems has now been well recognized. We consider in this book the concept of "intelligent manufacturing" as the application of soft computing techniques and fractal theory for achieving the goals of manufacturing, which are production planning and control, monitoring and diagnosis of faults, and automated quality control. As a prelude, we provide a brief overview of the existing methodologies in Soft Computing. We then describe our own approach in dealing with the problems in achieving intelligent manufacturing. Our particular point of view is that to really achieve intelligent manufacturing in real-world applications we need to use SC techniques and fractal theory.
Book Synopsis Extremes and Recurrence in Dynamical Systems by : Valerio Lucarini
Download or read book Extremes and Recurrence in Dynamical Systems written by Valerio Lucarini and published by John Wiley & Sons. This book was released on 2016-03-28 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by a team of international experts, Extremes and Recurrence in Dynamical Systems presents a unique point of view on the mathematical theory of extremes and on its applications in the natural and social sciences. Featuring an interdisciplinary approach to new concepts in pure and applied mathematical research, the book skillfully combines the areas of statistical mechanics, probability theory, measure theory, dynamical systems, statistical inference, geophysics, and software application. Emphasizing the statistical mechanical point of view, the book introduces robust theoretical embedding for the application of extreme value theory in dynamical systems. Extremes and Recurrence in Dynamical Systems also features: • A careful examination of how a dynamical system can serve as a generator of stochastic processes • Discussions on the applications of statistical inference in the theoretical and heuristic use of extremes • Several examples of analysis of extremes in a physical and geophysical context • A final summary of the main results presented along with a guide to future research projects • An appendix with software in Matlab® programming language to help readers to develop further understanding of the presented concepts Extremes and Recurrence in Dynamical Systems is ideal for academics and practitioners in pure and applied mathematics, probability theory, statistics, chaos, theoretical and applied dynamical systems, statistical mechanics, geophysical fluid dynamics, geosciences and complexity science. VALERIO LUCARINI, PhD, is Professor of Theoretical Meteorology at the University of Hamburg, Germany and Professor of Statistical Mechanics at the University of Reading, UK. DAVIDE FARANDA, PhD, is Researcher at the Laboratoire des science du climat et de l’environnement, IPSL, CEA Saclay, Université Paris-Saclay, Gif-sur-Yvette, France. ANA CRISTINA GOMES MONTEIRO MOREIRA DE FREITAS, PhD, is Assistant Professor in the Faculty of Economics at the University of Porto, Portugal. JORGE MIGUEL MILHAZES DE FREITAS, PhD, is Assistant Professor in the Department of Mathematics of the Faculty of Sciences at the University of Porto, Portugal. MARK HOLLAND, PhD, is Senior Lecturer in Applied Mathematics in the College of Engineering, Mathematics and Physical Sciences at the University of Exeter, UK. TOBIAS KUNA, PhD, is Associate Professor in the Department of Mathematics and Statistics at the University of Reading, UK. MATTHEW NICOL, PhD, is Professor of Mathematics at the University of Houston, USA. MIKE TODD, PhD, is Lecturer in the School of Mathematics and Statistics at the University of St. Andrews, Scotland. SANDRO VAIENTI, PhD, is Professor of Mathematics at the University of Toulon and Researcher at the Centre de Physique Théorique, France.
Book Synopsis Data Analysis for Direct Numerical Simulations of Turbulent Combustion by : Heinz Pitsch
Download or read book Data Analysis for Direct Numerical Simulations of Turbulent Combustion written by Heinz Pitsch and published by Springer Nature. This book was released on 2020-05-28 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents methodologies for analysing large data sets produced by the direct numerical simulation (DNS) of turbulence and combustion. It describes the development of models that can be used to analyse large eddy simulations, and highlights both the most common techniques and newly emerging ones. The chapters, written by internationally respected experts, invite readers to consider DNS of turbulence and combustion from a formal, data-driven standpoint, rather than one led by experience and intuition. This perspective allows readers to recognise the shortcomings of existing models, with the ultimate goal of quantifying and reducing model-based uncertainty. In addition, recent advances in machine learning and statistical inferences offer new insights on the interpretation of DNS data. The book will especially benefit graduate-level students and researchers in mechanical and aerospace engineering, e.g. those with an interest in general fluid mechanics, applied mathematics, and the environmental and atmospheric sciences.
