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Bifurcation And Chaos
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Book Synopsis Global Bifurcations and Chaos by : Stephen Wiggins
Download or read book Global Bifurcations and Chaos written by Stephen Wiggins and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: Global Bifurcations and Chaos: Analytical Methods is unique in the literature of chaos in that it not only defines the concept of chaos in deterministic systems, but it describes the mechanisms which give rise to chaos (i.e., homoclinic and heteroclinic motions) and derives explicit techniques whereby these mechanisms can be detected in specific systems. These techniques can be viewed as generalizations of Melnikov's method to multi-degree of freedom systems subject to slowly varying parameters and quasiperiodic excitations. A unique feature of the book is that each theorem is illustrated with drawings that enable the reader to build visual pictures of global dynamcis of the systems being described. This approach leads to an enhanced intuitive understanding of the theory.
Book Synopsis Chaos, Bifurcations And Fractals Around Us: A Brief Introduction by : Wanda Szemplinska-stupnicka
Download or read book Chaos, Bifurcations And Fractals Around Us: A Brief Introduction written by Wanda Szemplinska-stupnicka and published by World Scientific. This book was released on 2003-11-11 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last twenty years, a large number of books on nonlinear chaotic dynamics in deterministic dynamical systems have appeared. These academic tomes are intended for graduate students and require a deep knowledge of comprehensive, advanced mathematics. There is a need for a book that is accessible to general readers, a book that makes it possible to get a good deal of knowledge about complex chaotic phenomena in nonlinear oscillators without deep mathematical study.Chaos, Bifurcations and Fractals Around Us: A Brief Introduction fills that gap. It is a very short monograph that, owing to geometric interpretation complete with computer color graphics, makes it easy to understand even very complex advanced concepts of chaotic dynamics. This invaluable publication is also addressed to lecturers in engineering departments who want to include selected nonlinear problems in full time courses on general mechanics, vibrations or physics so as to encourage their students to conduct further study.
Book Synopsis Attractors, Bifurcations, & Chaos by : Tönu Puu
Download or read book Attractors, Bifurcations, & Chaos written by Tönu Puu and published by Springer Science & Business Media. This book was released on 2003-07-10 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: Attractors, Bifurcations, & Chaos - now in its second edition - begins with an introduction to mathematical methods in modern nonlinear dynamics and deals with differential equations. Phenomena such as bifurcations and deterministic chaos are given considerable emphasis, both in the methodological part, and in the second part, containing various applications in economics and in regional science. Coexistence of attractors and the multiplicity of development paths in nonlinear systems are central topics. The applications focus on issues such as business cycles, oligopoly, interregional trade dynamics, and economic development theory.
Book Synopsis Bifurcation and Chaos in Nonsmooth Mechanical Systems by : Jan Awrejcewicz
Download or read book Bifurcation and Chaos in Nonsmooth Mechanical Systems written by Jan Awrejcewicz and published by World Scientific. This book was released on 2003 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the theoretical frame for studying lumped nonsmooth dynamical systems: the mathematical methods are recalled, and adapted numerical methods are introduced (differential inclusions, maximal monotone operators, Filippov theory, Aizerman theory, etc.). Tools available for the analysis of classical smooth nonlinear dynamics (stability analysis, the Melnikov method, bifurcation scenarios, numerical integrators, solvers, etc.) are extended to the nonsmooth frame. Many models and applications arising from mechanical engineering, electrical circuits, material behavior and civil engineering are investigated to illustrate theoretical and computational developments.
Book Synopsis Bifurcation And Chaos In Simple Dynamical Systems by : Jan Awrejcewicz
Download or read book Bifurcation And Chaos In Simple Dynamical Systems written by Jan Awrejcewicz and published by World Scientific. This book was released on 1989-10-01 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a detailed analysis of bifurcation and chaos in simple non-linear systems, based on previous works of the author. Practical examples for mechanical and biomechanical systems are discussed. The use of both numerical and analytical approaches allows for a deeper insight into non-linear dynamical phenomena. The numerical and analytical techniques presented do not require specific mathematical knowledge.
Book Synopsis Discrete Dynamical Systems, Bifurcations and Chaos in Economics by : Wei-Bin Zhang
Download or read book Discrete Dynamical Systems, Bifurcations and Chaos in Economics written by Wei-Bin Zhang and published by Elsevier. This book was released on 2006-01-05 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a unique blend of difference equations theory and its exciting applications to economics. It deals with not only theory of linear (and linearized) difference equations, but also nonlinear dynamical systems which have been widely applied to economic analysis in recent years. It studies most important concepts and theorems in difference equations theory in a way that can be understood by anyone who has basic knowledge of calculus and linear algebra. It contains well-known applications and many recent developments in different fields of economics. The book also simulates many models to illustrate paths of economic dynamics. - A unique book concentrated on theory of discrete dynamical systems and its traditional as well as advanced applications to economics - Mathematical definitions and theorems are introduced in a systematic and easily accessible way - Examples are from almost all fields of economics; technically proceeding from basic to advanced topics - Lively illustrations with numerous figures - Numerous simulation to see paths of economic dynamics - Comprehensive treatment of the subject with a comprehensive and easily accessible approach
Book Synopsis Differential Equations, Bifurcations, and Chaos in Economics by : Wei-Bin Zhang
Download or read book Differential Equations, Bifurcations, and Chaos in Economics written by Wei-Bin Zhang and published by World Scientific. This book was released on 2005 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although the application of differential equations to economics is a vast and vibrant area, the subject has not been systematically studied; it is often treated as a subsidiary part of mathematical economics textbooks. This book aims to fill that void by providing a unique blend of the theory of differential equations and their exciting applications to dynamic economics. Containing not just a comprehensive introduction to the applications of the theory of linear (and linearized) differential equations to economic analysis, the book also studies nonlinear dynamical systems, which have only been widely applied to economic analysis in recent years. It provides comprehensive coverage of the most important concepts and theorems in the theory of differential equations in a way that can be understood by any reader who has a basic knowledge of calculus and linear algebra. In addition to traditional applications of the theory to economic dynamics, the book includes many recent developments in different fields of economics.
Book Synopsis The Lorenz Equations by : Colin Sparrow
Download or read book The Lorenz Equations written by Colin Sparrow and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: The equations which we are going to study in these notes were first presented in 1963 by E. N. Lorenz. They define a three-dimensional system of ordinary differential equations that depends on three real positive parameters. As we vary the parameters, we change the behaviour of the flow determined by the equations. For some parameter values, numerically computed solutions of the equations oscillate, apparently forever, in the pseudo-random way we now call "chaotic"; this is the main reason for the immense amount of interest generated by the equations in the eighteen years since Lorenz first presented them. In addition, there are some parameter values for which we see "preturbulence", a phenomenon in which trajectories oscillate chaotically for long periods of time before finally settling down to stable stationary or stable periodic behaviour, others in which we see "intermittent chaos", where trajectories alternate be tween chaotic and apparently stable periodic behaviours, and yet others in which we see "noisy periodicity", where trajectories appear chaotic though they stay very close to a non-stable periodic orbit. Though the Lorenz equations were not much studied in the years be tween 1963 and 1975, the number of man, woman, and computer hours spent on them in recent years - since they came to the general attention of mathematicians and other researchers - must be truly immense.
Book Synopsis Attractors, Bifurcations, and Chaos by : Tönu Puu
Download or read book Attractors, Bifurcations, and Chaos written by Tönu Puu and published by Springer. This book was released on 2014-10-03 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: Attractors, Bifurcations, & Chaos - now in its second edition - begins with an introduction to mathematical methods in modern nonlinear dynamics and deals with differential equations. Phenomena such as bifurcations and deterministic chaos are given considerable emphasis, both in the methodological part, and in the second part, containing various applications in economics and in regional science. Coexistence of attractors and the multiplicity of development paths in nonlinear systems are central topics. The applications focus on issues such as business cycles, oligopoly, interregional trade dynamics, and economic development theory.
Book Synopsis Nonlinear Phenomena in Power Electronics by : Soumitro Banerjee
Download or read book Nonlinear Phenomena in Power Electronics written by Soumitro Banerjee and published by Wiley-IEEE Press. This book was released on 2001-07-16 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Brings the knowledge of 24 experts in this maturing field out from the narrow confines of academic circles, and makes it accessible to graduate students and power electronics professionals alike. * Provides practicing engineers with the knowledge to predict power requirement behavior. * The insights gained from this all-inclusive compilation will ultimately lead to better design methodologies.
Book Synopsis Nonlinear Dynamics and Chaos by : Steven H. Strogatz
Download or read book Nonlinear Dynamics and Chaos written by Steven H. Strogatz and published by CRC Press. This book was released on 2018-05-04 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.
Book Synopsis Bifurcation Control by : Guanrong Chen
Download or read book Bifurcation Control written by Guanrong Chen and published by Springer Science & Business Media. This book was released on 2003-08-26 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bifurcation control refers to the task of designing a controller that can modify the bifurcation properties of a given nonlinear system, so as to achieve some desirable dynamical behaviors. There exists no similar control theory-oriented book available in the market that is devoted to the subject of bifurcation control, written by control engineers for control engineers. World-renowned leading experts in the field provide their state-of-the-art survey about the extensive research that has been done over the last few years in this subject. The book is not only aimed at active researchers in the field of bifurcation control and its applications, but also at a general audience in related fields.
Book Synopsis Practical Bifurcation and Stability Analysis by : Rüdiger U. Seydel
Download or read book Practical Bifurcation and Stability Analysis written by Rüdiger U. Seydel and published by Springer Science & Business Media. This book was released on 2009-11-27 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probably the first book to describe computational methods for numerically computing steady state and Hopf bifurcations. Requiring only a basic knowledge of calculus, and using detailed examples, problems, and figures, this is an ideal textbook for graduate students.
Book Synopsis Controlling Chaos and Bifurcations in Engineering Systems by : Guanrong Chen
Download or read book Controlling Chaos and Bifurcations in Engineering Systems written by Guanrong Chen and published by CRC Press. This book was released on 1999-09-28 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last two decades, chaos in engineering systems has moved from being simply a curious phenomenon to one with real, practical significance and utility. Engineers, scientists, and mathematicians have similarly advanced from the passive role of analyzing chaos to their present, active role of controlling chaos-control directed not only at suppression, but also at exploiting its enormous potential. We now stand at the threshold of major advances in the control and synchronization of chaos for new applications across the range of engineering disciplines. Controlling Chaos and Bifurcations in Engineering Systems provides a state-of-the-art survey of the control-and anti-control-of chaos in dynamical systems. Internationally known experts in the field join forces in this volume to form this tutorial-style combination of overview and technical report on the latest advances in the theory and applications of chaos control. They detail various approaches to control and show how designers can use chaos to create a wider variety of properties and greater flexibility in the design process. Chaos control promises to have a major impact on novel time- and energy-critical engineering applications. Within this volume, readers will find many challenging problems-yet unsolved-regarding both the fundamental theory and potential applications of chaos control and anti-control. Controlling Chaos and Bifurcations in Engineering Systems will bring readers up-to-date on recent development in the field and help open the door to new advances.
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 Stability, Instability and Chaos by : Paul Glendinning
Download or read book Stability, Instability and Chaos written by Paul Glendinning and published by Cambridge University Press. This book was released on 1994-11-25 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to nonlinear differential equations which equips undergraduate students with the know-how to appreciate stability theory and bifurcation.
Download or read book Chaos written by Kathleen Alligood and published by Springer. This book was released on 2012-12-06 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: BACKGROUND Sir Isaac Newton hrought to the world the idea of modeling the motion of physical systems with equations. It was necessary to invent calculus along the way, since fundamental equations of motion involve velocities and accelerations, of position. His greatest single success was his discovery that which are derivatives the motion of the planets and moons of the solar system resulted from a single fundamental source: the gravitational attraction of the hodies. He demonstrated that the ohserved motion of the planets could he explained hy assuming that there is a gravitational attraction he tween any two ohjects, a force that is proportional to the product of masses and inversely proportional to the square of the distance between them. The circular, elliptical, and parabolic orhits of astronomy were v INTRODUCTION no longer fundamental determinants of motion, but were approximations of laws specified with differential equations. His methods are now used in modeling motion and change in all areas of science. Subsequent generations of scientists extended the method of using differ ential equations to describe how physical systems evolve. But the method had a limitation. While the differential equations were sufficient to determine the behavior-in the sense that solutions of the equations did exist-it was frequently difficult to figure out what that behavior would be. It was often impossible to write down solutions in relatively simple algebraic expressions using a finite number of terms. Series solutions involving infinite sums often would not converge beyond some finite time.
