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Hyperbolic Chaos
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Book Synopsis Hyperbolic Chaos by : Sergey P. Kuznetsov
Download or read book Hyperbolic Chaos written by Sergey P. Kuznetsov and published by Springer Science & Business Media. This book was released on 2012-03-20 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Hyperbolic Chaos: A Physicist’s View” presents recent progress on uniformly hyperbolic attractors in dynamical systems from a physical rather than mathematical perspective (e.g. the Plykin attractor, the Smale – Williams solenoid). The structurally stable attractors manifest strong stochastic properties, but are insensitive to variation of functions and parameters in the dynamical systems. Based on these characteristics of hyperbolic chaos, this monograph shows how to find hyperbolic chaotic attractors in physical systems and how to design a physical systems that possess hyperbolic chaos. This book is designed as a reference work for university professors and researchers in the fields of physics, mechanics, and engineering. Dr. Sergey P. Kuznetsov is a professor at the Department of Nonlinear Processes, Saratov State University, Russia.
Book Synopsis Nonlinear Dynamics and Chaos by : J. M. T. Thompson
Download or read book Nonlinear Dynamics and Chaos written by J. M. T. Thompson and published by John Wiley & Sons. This book was released on 2002-02-15 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ein angesehener Bestseller - jetzt in der 2.aktualisierten Auflage! In diesem Buch finden Sie die aktuellsten Forschungsergebnisse auf dem Gebiet nichtlinearer Dynamik und Chaos, einem der am schnellsten wachsenden Teilgebiete der Mathematik. Die seit der ersten Auflage hinzugekommenen Erkenntnisse sind in einem zusätzlichen Kapitel übersichtlich zusammengefasst.
Book Synopsis Robust Chaos and Its Applications by : Elhadj Zeraoulia
Download or read book Robust Chaos and Its Applications written by Elhadj Zeraoulia and published by World Scientific. This book was released on 2012 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robust chaos is defined by the absence of periodic windows and coexisting attractors in some neighborhoods in the parameter space of a dynamical system. This unique book explores the definition, sources, and roles of robust chaos. The book is written in a reasonably self-contained manner and aims to provide students and researchers with the necessary understanding of the subject. Most of the known results, experiments, and conjectures about chaos in general and about robust chaos in particular are collected here in a pedagogical form. Many examples of dynamical systems, ranging from purely mathematical to natural and social processes displaying robust chaos, are discussed in detail. At the end of each chapter is a set of exercises and open problems (more than 260 in the whole book) intended to reinforce the ideas and provide additional experiences for both readers and researchers in nonlinear science in general, and chaos theory in particular.
Book Synopsis Polynomial Chaos Methods for Hyperbolic Partial Differential Equations by : Mass Per Pettersson
Download or read book Polynomial Chaos Methods for Hyperbolic Partial Differential Equations written by Mass Per Pettersson and published by Springer. This book was released on 2015-03-10 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents computational techniques and numerical analysis to study conservation laws under uncertainty using the stochastic Galerkin formulation. With the continual growth of computer power, these methods are becoming increasingly popular as an alternative to more classical sampling-based techniques. The text takes advantage of stochastic Galerkin projections applied to the original conservation laws to produce a large system of modified partial differential equations, the solutions to which directly provide a full statistical characterization of the effect of uncertainties. Polynomial Chaos Methods of Hyperbolic Partial Differential Equations focuses on the analysis of stochastic Galerkin systems obtained for linear and non-linear convection-diffusion equations and for a systems of conservation laws; a detailed well-posedness and accuracy analysis is presented to enable the design of robust and stable numerical methods. The exposition is restricted to one spatial dimension and one uncertain parameter as its extension is conceptually straightforward. The numerical methods designed guarantee that the solutions to the uncertainty quantification systems will converge as the mesh size goes to zero. Examples from computational fluid dynamics are presented together with numerical methods suitable for the problem at hand: stable high-order finite-difference methods based on summation-by-parts operators for smooth problems, and robust shock-capturing methods for highly nonlinear problems. Academics and graduate students interested in computational fluid dynamics and uncertainty quantification will find this book of interest. Readers are expected to be familiar with the fundamentals of numerical analysis. Some background in stochastic methods is useful but notnecessary.
Book Synopsis Hyperbolic Chaos by : Sergej P. Kuznecov
Download or read book Hyperbolic Chaos written by Sergej P. Kuznecov and published by . This book was released on 2012 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Collection of Papers on Chaos Theory and Its Applications by : Paul Bracken
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.
Book Synopsis Frontiers in the Study of Chaotic Dynamical Systems with Open Problems by : Elhadj Zeraoulia
Download or read book Frontiers in the Study of Chaotic Dynamical Systems with Open Problems written by Elhadj Zeraoulia and published by World Scientific. This book was released on 2011 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of review articles is devoted to new developments in the study of chaotic dynamical systems with some open problems and challenges. The papers, written by many of the leading experts in the field, cover both the experimental and theoretical aspects of the subject. This edited volume presents a variety of fascinating topics of current interest and problems arising in the study of both discrete and continuous time chaotic dynamical systems. Exciting new techniques stemming from the area of nonlinear dynamical systems theory are currently being developed to meet these challenges. Presenting the state-of-the-art of the more advanced studies of chaotic dynamical systems, Frontiers in the Study of Chaotic Dynamical Systems with Open Problems is devoted to setting an agenda for future research in this exciting and challenging field.
Download or read book Chaos Near Resonance written by G. Haller and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unified treatment of resonant problems with special emphasis on the recently discovered phenomenon of homoclinic jumping. After a survey of the necessary background, the book develops a general finite dimensional theory of homoclinic jumping, illustrating it with examples. The main mechanism of chaos near resonances is discussed in both the dissipative and the Hamiltonian context, incorporating previously unpublished new results on universal homoclinic bifurcations near resonances, as well as on multi-pulse Silnikov manifolds. The results are applied to a variety of different problems, which include applications from beam oscillations, surface wave dynamics, nonlinear optics, atmospheric science and fluid mechanics.
Download or read book Chaos written by Otto E. Rössler and published by Springer Nature. This book was released on 2020-05-20 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written in the 1980s by one of the fathers of chaos theory, Otto E. Rössler, the manuscript presented in this volume eventually never got published. Almost 40 years later, it remains astonishingly at the forefront of knowledge about chaos theory and many of the examples discussed have never been published elsewhere. The manuscript has now been edited by Christophe Letellier - involved in chaos theory for almost three decades himself, as well as being active in the history of sciences - with a minimum of changes to the original text. Finally released for the benefit of specialists and non-specialists alike, this book is equally interesting from the historical and the scientific points of view: an unconventionally modern approach to chaos theory, it can be read as a classic introduction and short monograph as well as a collection of original insights into advanced topics from this field.
Book Synopsis Nonlinear Dynamics of Chaotic and Stochastic Systems by : Vadim S. Anishchenko
Download or read book Nonlinear Dynamics of Chaotic and Stochastic Systems written by Vadim S. Anishchenko and published by Springer Science & Business Media. This book was released on 2007-07-20 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present an improved and enlarged version of our book Nonlinear - namics of Chaotic and Stochastic Systems published by Springer in 2002. Basically, the new edition of the book corresponds to its ?rst version. While preparingthiseditionwemadesomeclari?cationsinseveralsectionsandalso corrected the misprints noticed in some formulas. Besides, three new sections have been added to Chapter 2. They are “Statistical Properties of Dynamical Chaos,” “E?ects of Synchronization in Extended Self-Sustained Oscillatory Systems,” and “Synchronization in Living Systems.” The sections indicated re?ect the most interesting results obtained by the authors after publication of the ?rst edition. We hope that the new edition of the book will be of great interest for a widesectionofreaderswhoarealreadyspecialistsorthosewhoarebeginning research in the ?elds of nonlinear oscillation and wave theory, dynamical chaos, synchronization, and stochastic process theory. Saratov, Berlin, and St. Louis V.S. Anishchenko November 2006 A.B. Neiman T.E. Vadiavasova V.V. Astakhov L. Schimansky-Geier Preface to the First Edition Thisbookisdevotedtotheclassicalbackgroundandtocontemporaryresults on nonlinear dynamics of deterministic and stochastic systems. Considerable attentionisgiventothee?ectsofnoiseonvariousregimesofdynamicsystems with noise-induced order. On the one hand, there exists a rich literature of excellent books on n- linear dynamics and chaos; on the other hand, there are many marvelous monographs and textbooks on the statistical physics of far-from-equilibrium andstochasticprocesses.Thisbookisanattempttocombinetheapproachof nonlinear dynamics based on the deterministic evolution equations with the approach of statistical physics based on stochastic or kinetic equations. One of our main aims is to show the important role of noise in the organization and properties of dynamic regimes of nonlinear dissipative systems.
Book Synopsis Path Integrals, Hyperbolic Spaces and Selberg Trace Formulae by : Christian Grosche
Download or read book Path Integrals, Hyperbolic Spaces and Selberg Trace Formulae written by Christian Grosche and published by World Scientific. This book was released on 2013-07-26 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this second edition, a comprehensive review is given for path integration in two- and three-dimensional (homogeneous) spaces of constant and non-constant curvature, including an enumeration of all the corresponding coordinate systems which allow separation of variables in the Hamiltonian and in the path integral. The corresponding path integral solutions are presented as a tabulation. Proposals concerning interbasis expansions for spheroidal coordinate systems are also given. In particular, the cases of non-constant curvature Darboux spaces are new in this edition. The volume also contains results on the numerical study of the properties of several integrable billiard systems in compact domains (i.e. rectangles, parallelepipeds, circles and spheres) in two- and three-dimensional flat and hyperbolic spaces. In particular, the discussions of integrable billiards in circles and spheres (flat and hyperbolic spaces) and in three dimensions are new in comparison to the first edition. In addition, an overview is presented on some recent achievements in the theory of the Selberg trace formula on Riemann surfaces, its super generalization, their use in mathematical physics and string theory, and some further results derived from the Selberg (super-) trace formula. Contents:IntroductionPath Integrals in Quantum MechanicsSeparable Coordinate Systems on Spaces of Constant CurvaturePath Integrals in Pseudo-Euclidean GeometryPath Integrals in Euclidean SpacesPath Integrals on SpheresPath Integrals on HyperboloidsPath Integral on the Complex SpherePath Integrals on Hermitian Hyperbolic SpacePath Integrals on Darboux SpacesPath Integrals on Single-Sheeted HyperboloidsMiscellaneous Results on Path IntegrationBilliard Systems and Periodic Orbit TheoryThe Selberg Trace FormulaThe Selberg Super-Trace FormulaSummary and Discussion Readership: Graduate and researchers in mathematical physics. Keywords:Path Integrals;Selberg Trace Formula;Quantum Chaos;Coordinate Systems;Homogeneous Spaces;Spaces of Non-Constant Curvature;Separation of VariablesKey Features:The 2nd edition brings the text up to date with new developments and results in the fieldContains enumeration of many explicit path integrals solutionsReviews: “This book is a good survey of results in a fascinating, highly geometrical, field in which much remains to be done.” Zentralblatt MATH
Book Synopsis Path Integrals, Hyperbolic Spaces and Selberg Trace Formulae by : Christian Grosche
Download or read book Path Integrals, Hyperbolic Spaces and Selberg Trace Formulae written by Christian Grosche and published by World Scientific. This book was released on 2013 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this second edition, a comprehensive review is given for path integration in two- and three-dimensional (homogeneous) spaces of constant and non-constant curvature, including an enumeration of all the corresponding coordinate systems which allow separation of variables in the Hamiltonian and in the path integral. The corresponding path integral solutions are presented as a tabulation. Proposals concerning interbasis expansions for spheroidal coordinate systems are also given. In particular, the cases of non-constant curvature Darboux spaces are new in this edition. The volume also contains results on the numerical study of the properties of several integrable billiard systems in compact domains (i.e. rectangles, parallelepipeds, circles and spheres) in two- and three-dimensional flat and hyperbolic spaces. In particular, the discussions of integrable billiards in circles and spheres (flat and hyperbolic spaces) and in three dimensions are new in comparison to the first edition. In addition, an overview is presented on some recent achievements in the theory of the Selberg trace formula on Riemann surfaces, its super generalization, their use in mathematical physics and string theory, and some further results derived from the Selberg (super-) trace formula.
Book Synopsis Toward Analytical Chaos in Nonlinear Systems by : Albert C. J. Luo
Download or read book Toward Analytical Chaos in Nonlinear Systems written by Albert C. J. Luo and published by John Wiley & Sons. This book was released on 2014-05-27 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exact analytical solutions to periodic motions in nonlineardynamical systems are almost not possible. Since the 18th century,one has extensively used techniques such as perturbation methods toobtain approximate analytical solutions of periodic motions innonlinear systems. However, the perturbation methods cannot providethe enough accuracy of analytical solutions of periodic motions innonlinear dynamical systems. So the bifurcation trees of periodicmotions to chaos cannot be achieved analytically. The authorhas developed an analytical technique that is more effective toachieve periodic motions and corresponding bifurcation trees tochaos analytically. Toward Analytical Chaos in Nonlinear Systemssystematically presents a new approach to analytically determineperiodic flows to chaos or quasi-periodic flows in nonlineardynamical systems with/without time-delay. It covers themathematical theory and includes two examples of nonlinear systemswith/without time-delay in engineering and physics. From theanalytical solutions, the routes from periodic motions to chaos aredeveloped analytically rather than the incomplete numerical routesto chaos. The analytical techniques presented will provide abetter understanding of regularity and complexity of periodicmotions and chaos in nonlinear dynamical systems. Key features: Presents the mathematical theory of analytical solutions ofperiodic flows to chaos or quasieriodic flows in nonlineardynamical systems Covers nonlinear dynamical systems and nonlinear vibrationsystems Presents accurate, analytical solutions of stable and unstableperiodic flows for popular nonlinear systems Includes two complete sample systems Discusses time-delayed, nonlinear systems and time-delayed,nonlinear vibrational systems Includes real world examples Toward Analytical Chaos in Nonlinear Systems is acomprehensive reference for researchers and practitioners acrossengineering, mathematics and physics disciplines, and is also auseful source of information for graduate and senior undergraduatestudents in these areas.
Book Synopsis Dissipative Structures and Chaos by : Hazime Mori
Download or read book Dissipative Structures and Chaos written by Hazime Mori and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of two parts, the first dealing with dissipative structures and the second with the structure and physics of chaos. The first part was written by Y. Kuramoto and the second part by H. Mori. Throughout the book, emphasis is laid on fundamental concepts and methods rather than applications, which are too numerous to be treated here. Typical physical examples, however, including nonlinear forced oscilla tors, chemical reactions with diffusion, and Benard convection in horizontal fluid layers, are discussed explicitly. Our consideration of dissipative structures is based on a phenomenolog ical reduction theory in which universal aspects of the phenomena under consideration are emphasized, while the theory of chaos is developed to treat transport phenomena, such as the mixing and diffusion of chaotic orbits, from the viewpoint of the geometrical phase space structure of chaos. The title of the original, Japanese version of the book is Sanitsu Kozo to Kaosu (Dissipative Structures and Chaos). It is part of the Iwanami Koza Gendai no Butsurigaku (Iwanami Series on Modern Physics). The first Japanese edition was published in March 1994 and the second in August 1997. We are pleased that this book has been translated into English and that it can now have an audience outside of Japan. We would like to express our gratitude to Glenn Paquette for his English translation, which has made this book more understandable than the original in many respects.
Book Synopsis Chua's Circuit: A Paradigm for Chaos by : Rabinder N Madan
Download or read book Chua's Circuit: A Paradigm for Chaos written by Rabinder N Madan and published by World Scientific. This book was released on 1993-11-20 with total page 1088 pages. Available in PDF, EPUB and Kindle. Book excerpt: For uninitiated researchers, engineers, and scientists interested in a quick entry into the subject of chaos, this book offers a timely collection of 55 carefully selected papers covering almost every aspect of this subject. Because Chua's circuit is endowed with virtually every bifurcation phenomena reported in the extensive literature on chaos, and because it is the only chaotic system which can be easily built by a novice, simulated in a personal computer, and tractable mathematically, it has become a paradigm for chaos, and a vehicle for illustrating this ubiquitous phenomenon. Its supreme simplicity and robustness has made it the circuit of choice for generating chaotic signals for practical applications. In addition to the 48 illuminating papers drawn from a recent two-part Special Issue (March and June, 1993) of the Journal of Circuits, Systems, and Computers devoted exclusively to Chua's circuit, several highly illustrative tutorials and incisive state-of-the-art reviews on the latest experimental, computational, and analytical investigations on chaos are also included. To enhance its pedagogical value, a diskette containing a user-friendly software and data base on many basic chaotic phenomena is attached to the book, as well as a gallery of stunningly colorful strange attractors. Beginning with an elementary (freshman-level physics) introduction on experimental chaos, the book presents a step-by-step guided tour, with papers of increasing complexity, which covers almost every conceivable aspects of bifurcation and chaos. The second half of the book contains many original materials contributed by world-renowned authorities on chaos, including L P Shil'nikov, A N Sharkovsky, M Misiurewicz, A I Mees, R Lozi, L O Chua and V S Afraimovich. The scope of topics covered is quite comprehensive, including at least one paper on each of the following topics: routes to chaos, 1-D maps, universality, self-similarity, 2-parameter renormalization group analysis, piecewise-linear dynamics, slow-fast dynamics, confinor analysis, symmetry breaking, strange attractors, basins of attraction, geometric invariants, time-series reconstruction, Lyapunov exponents, bispectral analysis, homoclinic bifurcation, stochastic resonance, synchronization, and control of chaos, as well as several novel applications of chaos, including secure communications, visual sensing, neural networks, dry turbulence, nonlinear waves and music. Contents:Bifurcation PhenomenaResonance, Synchronization, and WavesApplications of Chua's CircuitControlling ChaosOne-Dimensional Poincaré Maps From Chua's CircuitStrange AttractorsPiecewise-Linear AnalysisTime Series AnalysisGeneralizations of Chua's Circuit Readership: Physicists, biologists, mathematicians, chemists, engineers and researchers on nonlinear science. keywords:
Book Synopsis Introduction to Applied Nonlinear Dynamical Systems and Chaos by : Stephen Wiggins
Download or read book Introduction to Applied Nonlinear Dynamical Systems and Chaos written by Stephen Wiggins and published by Springer Science & Business Media. This book was released on 2003-10-01 with total page 860 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to applied nonlinear dynamics and chaos places emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about their behavior. The new edition has been updated and extended throughout, and contains a detailed glossary of terms. From the reviews: "Will serve as one of the most eminent introductions to the geometric theory of dynamical systems." --Monatshefte für Mathematik
Book Synopsis 2-D Quadratic Maps and 3-D ODE Systems by :
Download or read book 2-D Quadratic Maps and 3-D ODE Systems written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
