Bifurcation Theory And Applications

Author : Wang Shouhong,Ma Tian
Publisher : World Scientific
Page : 392 pages
File Size : 49,9 Mb
Release : 2005-06-27
Category : Science
ISBN : 9789814480598

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Bifurcation Theory And Applications by Wang Shouhong,Ma Tian Pdf

This book covers comprehensive bifurcation theory and its applications to dynamical systems and partial differential equations (PDEs) from science and engineering, including in particular PDEs from physics, chemistry, biology, and hydrodynamics.The book first introduces bifurcation theories recently developed by the authors, on steady state bifurcation for a class of nonlinear problems with even order nondegenerate nonlinearities, regardless of the multiplicity of the eigenvalues, and on attractor bifurcations for nonlinear evolution equations, a new notion of bifurcation.With this new notion of bifurcation, many longstanding bifurcation problems in science and engineering are becoming accessible, and are treated in the second part of the book. In particular, applications are covered for a variety of PDEs from science and engineering, including the Kuramoto-Sivashinsky equation, the Cahn-Hillard equation, the Ginzburg-Landau equation, reaction-diffusion equations in biology and chemistry, the Benard convection problem, and the Taylor problem. The applications provide, on the one hand, general recipes for other applications of the theory addressed in this book, and on the other, full classifications of the bifurcated attractor and the global attractor as the control parameters cross certain critical values, dictated usually by the eigenvalues of the linearized problems. It is expected that the book will greatly advance the study of nonlinear dynamics for many problems in science and engineering.

Author : Hansjörg Kielhöfer
Publisher : Springer Science & Business Media
Page : 355 pages
File Size : 49,6 Mb
Release : 2006-04-10
Category : Mathematics
ISBN : 9780387216331

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Bifurcation Theory by Hansjörg Kielhöfer Pdf

In the past three decades, bifurcation theory has matured into a well-established and vibrant branch of mathematics. This book gives a unified presentation in an abstract setting of the main theorems in bifurcation theory, as well as more recent and lesser known results. It covers both the local and global theory of one-parameter bifurcations for operators acting in infinite-dimensional Banach spaces, and shows how to apply the theory to problems involving partial differential equations. In addition to existence, qualitative properties such as stability and nodal structure of bifurcating solutions are treated in depth. This volume will serve as an important reference for mathematicians, physicists, and theoretically-inclined engineers working in bifurcation theory and its applications to partial differential equations.

Author : Yuri Kuznetsov
Publisher : Springer Science & Business Media
Page : 648 pages
File Size : 47,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475739787

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Elements of Applied Bifurcation Theory by Yuri Kuznetsov Pdf

Providing readers with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems, the focus here is on efficient numerical implementations of the developed techniques. The book is designed for advanced undergraduates or graduates in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the first while updating the context to incorporate recent theoretical developments, in particular new and improved numerical methods for bifurcation analysis.

Author : Guanrong Chen,David John Hill,Xinghuo Yu
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 55,5 Mb
Release : 2003-08-26
Category : Technology & Engineering
ISBN : 3540403418

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Bifurcation Control by Guanrong Chen,David John Hill,Xinghuo Yu Pdf

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.

Author : Shangjiang Guo,Jianhong Wu
Publisher : Springer Science & Business Media
Page : 295 pages
File Size : 41,7 Mb
Release : 2013-07-30
Category : Mathematics
ISBN : 9781461469926

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Bifurcation Theory of Functional Differential Equations by Shangjiang Guo,Jianhong Wu Pdf

This book provides a crash course on various methods from the bifurcation theory of Functional Differential Equations (FDEs). FDEs arise very naturally in economics, life sciences and engineering and the study of FDEs has been a major source of inspiration for advancement in nonlinear analysis and infinite dimensional dynamical systems. The book summarizes some practical and general approaches and frameworks for the investigation of bifurcation phenomena of FDEs depending on parameters with chap. This well illustrated book aims to be self contained so the readers will find in this book all relevant materials in bifurcation, dynamical systems with symmetry, functional differential equations, normal forms and center manifold reduction. This material was used in graduate courses on functional differential equations at Hunan University (China) and York University (Canada).

Author : G‚rard Iooss,Moritz Adelmeyer
Publisher : World Scientific
Page : 204 pages
File Size : 43,6 Mb
Release : 1998
Category : Technology & Engineering
ISBN : 9810237286

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Topics in Bifurcation Theory and Applications by G‚rard Iooss,Moritz Adelmeyer Pdf

This textbook presents the most efficient analytical techniques in the local bifurcation theory of vector fields. It is centered on the theory of normal forms and its applications, including interaction with symmetries. The first part of the book reviews the center manifold reduction and introduces normal forms (with complete proofs). Basic bifurcations are studied together with bifurcations in the presence of symmetries. Special attention is given to examples with reversible vector fields, including the physical example given by the water waves. In this second edition, many problems with detailed solutions are added at the end of the first part (some systems being in infinite dimensions). The second part deals with the Couette-Taylor hydrodynamical stability problem, between concentric rotating cylinders. The spatial structure of various steady or unsteady solutions results directly from the analysis of the reduced system on a center manifold. In this part we also study bifurcations (simple here) from group orbits of solutions in an elementary way (avoiding heavy algebra). The third part analyzes bifurcations from time periodic solutions of autonomous vector fields. A normal form theory is developed, covering all cases, and emphasizing a partial Floquet reduction theory, which is applicable in infinite dimensions. Studies of period doubling as well as Arnold's resonance tongues are included in this part.

Author : Gerard Iooss,Daniel D. Joseph
Publisher : Springer Science & Business Media
Page : 347 pages
File Size : 51,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461209973

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Elementary Stability and Bifurcation Theory by Gerard Iooss,Daniel D. Joseph Pdf

This substantially revised second edition teaches the bifurcation of asymptotic solutions to evolution problems governed by nonlinear differential equations. Written not just for mathematicians, it appeals to the widest audience of learners, including engineers, biologists, chemists, physicists and economists. For this reason, it uses only well-known methods of classical analysis at foundation level, while the applications and examples are specially chosen to be as varied as possible.

Author : Tian Ma,Shouhong Wang
Publisher : World Scientific
Page : 391 pages
File Size : 42,5 Mb
Release : 2005
Category : Mathematics
ISBN : 9789812701152

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Bifurcation Theory and Applications by Tian Ma,Shouhong Wang Pdf

This book covers comprehensive bifurcation theory and its applications to dynamical systems and partial differential equations (PDEs) from science and engineering, including in particular PDEs from physics, chemistry, biology, and hydrodynamics. The book first introduces bifurcation theories recently developed by the authors, on steady state bifurcation for a class of nonlinear problems with even order nondegenerate nonlinearities, regardless of the multiplicity of the eigenvalues, and on attractor bifurcations for nonlinear evolution equations, a new notion of bifurcation. With this new notion of bifurcation, many longstanding bifurcation problems in science and engineering are becoming accessible, and are treated in the second part of the book. In particular, applications are covered for a variety of PDEs from science and engineering, including the KuramotoOCoSivashinsky equation, the CahnOCoHillard equation, the GinzburgOCoLandau equation, reaction-diffusion equations in biology and chemistry, the Benard convection problem, and the Taylor problem. The applications provide, on the one hand, general recipes for other applications of the theory addressed in this book, and on the other, full classifications of the bifurcated attractor and the global attractor as the control parameters cross certain critical values, dictated usually by the eigenvalues of the linearized problems. It is expected that the book will greatly advance the study of nonlinear dynamics for many problems in science and engineering."

Author : Paul H. Rabinowitz
Publisher : Unknown
Page : 408 pages
File Size : 52,8 Mb
Release : 1977
Category : Mathematics
ISBN : UOM:39015026152259

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Applications of Bifurcation Theory by Paul H. Rabinowitz Pdf

Author : Gérard Iooss,Moritz Adelmeyer
Publisher : World Scientific Publishing Company
Page : 196 pages
File Size : 50,8 Mb
Release : 1999-01-22
Category : Science
ISBN : 9789813105348

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Topics in Bifurcation Theory and Applications by Gérard Iooss,Moritz Adelmeyer Pdf

This textbook presents the most efficient analytical techniques in the local bifurcation theory of vector fields. It is centered on the theory of normal forms and its applications, including interaction with symmetries. The first part of the book reviews the center manifold reduction and introduces normal forms (with complete proofs). Basic bifurcations are studied together with bifurcations in the presence of symmetries. Special attention is given to examples with reversible vector fields, including the physical example given by the water waves. In this second edition, many problems with detailed solutions are added at the end of the first part (some systems being in infinite dimensions). The second part deals with the Couette–Taylor hydrodynamical stability problem, between concentric rotating cylinders. The spatial structure of various steady or unsteady solutions results directly from the analysis of the reduced system on a center manifold. In this part we also study bifurcations (simple here) from group orbits of solutions in an elementary way (avoiding heavy algebra). The third part analyzes bifurcations from time periodic solutions of autonomous vector fields. A normal form theory is developed, covering all cases, and emphasizing a partial Floquet reduction theory, which is applicable in infinite dimensions. Studies of period doubling as well as Arnold's resonance tongues are included in this part.

Author : J. E. Marsden,M. McCracken
Publisher : Springer Science & Business Media
Page : 420 pages
File Size : 41,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461263746

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The Hopf Bifurcation and Its Applications by J. E. Marsden,M. McCracken Pdf

The goal of these notes is to give a reasonahly com plete, although not exhaustive, discussion of what is commonly referred to as the Hopf bifurcation with applications to spe cific problems, including stability calculations. Historical ly, the subject had its origins in the works of Poincare [1] around 1892 and was extensively discussed by Andronov and Witt [1] and their co-workers starting around 1930. Hopf's basic paper [1] appeared in 1942. Although the term "Poincare Andronov-Hopf bifurcation" is more accurate (sometimes Friedrichs is also included), the name "Hopf Bifurcation" seems more common, so we have used it. Hopf's crucial contribution was the extension from two dimensions to higher dimensions. The principal technique employed in the body of the text is that of invariant manifolds. The method of Ruelle Takens [1] is followed, with details, examples and proofs added. Several parts of the exposition in the main text come from papers of P. Chernoff, J. Dorroh, O. Lanford and F. Weissler to whom we are grateful. The general method of invariant manifolds is common in dynamical systems and in ordinary differential equations: see for example, Hale [1,2] and Hartman [1]. Of course, other methods are also available. In an attempt to keep the picture balanced, we have included samples of alternative approaches. Specifically, we have included a translation (by L. Howard and N. Kopell) of Hopf's original (and generally unavailable) paper.

Author : Kiyohiro Ikeda,Kazuo Murota
Publisher : Springer Science & Business Media
Page : 436 pages
File Size : 46,6 Mb
Release : 2002-05-31
Category : Science
ISBN : 0387954090

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Imperfect Bifurcation in Structures and Materials by Kiyohiro Ikeda,Kazuo Murota Pdf

Most physical systems lose or gain stability through bifurcation behavior. This book explains a series of experimentally found bifurcation phenomena by means of the methods of static bifurcation theory.

Author : Mario Bernardo,Chris Budd,Alan Richard Champneys,Piotr Kowalczyk
Publisher : Springer Science & Business Media
Page : 497 pages
File Size : 40,7 Mb
Release : 2008-01-01
Category : Mathematics
ISBN : 9781846287084

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Piecewise-smooth Dynamical Systems by Mario Bernardo,Chris Budd,Alan Richard Champneys,Piotr Kowalczyk Pdf

This book presents a coherent framework for understanding the dynamics of piecewise-smooth and hybrid systems. An informal introduction expounds the ubiquity of such models via numerous. The results are presented in an informal style, and illustrated with many examples. The book is aimed at a wide audience of applied mathematicians, engineers and scientists at the beginning postgraduate level. Almost no mathematical background is assumed other than basic calculus and algebra.

Author : V.I. Arnold,V.S. Afrajmovich,Yu.S. Il'yashenko,L.P. Shil'nikov
Publisher : Springer Science & Business Media
Page : 279 pages
File Size : 55,7 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9783642578847

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Dynamical Systems V by V.I. Arnold,V.S. Afrajmovich,Yu.S. Il'yashenko,L.P. Shil'nikov Pdf

Bifurcation theory and catastrophe theory are two well-known areas within the field of dynamical systems. Both are studies of smooth systems, focusing on properties that seem to be manifestly non-smooth. Bifurcation theory is concerned with the sudden changes that occur in a system when one or more parameters are varied. Examples of such are familiar to students of differential equations, from phase portraits. Understanding the bifurcations of the differential equations that describe real physical systems provides important information about the behavior of the systems. Catastrophe theory became quite famous during the 1970's, mostly because of the sensation caused by the usually less than rigorous applications of its principal ideas to "hot topics", such as the characterization of personalities and the difference between a "genius" and a "maniac". Catastrophe theory is accurately described as singularity theory and its (genuine) applications. The authors of this book, previously published as Volume 5 of the Encyclopaedia, have given a masterly exposition of these two theories, with penetrating insight.

Author : Jan Awrejcewicz
Publisher : Springer
Page : 296 pages
File Size : 43,8 Mb
Release : 1995
Category : Computers
ISBN : UOM:39015034417280

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Bifurcation and Chaos by Jan Awrejcewicz Pdf

Bifurcation and Chaos presents a collection of especially written articles describing the theory and application of nonlinear dynamics to a wide variety of problems encountered in physics and engineering. Each chapter is self-contained and includes an elementary introduction, an exposition of the present state of the art, and details of recent theoretical, computational and experimental results. Included among the practical systems analysed are: hysteretic circuits, Josephson circuits, magnetic systems, railway dynamics, rotor dynamics and nonlinear dynamics of speech. This book contains important information and ideas for all mathematicians, physicists and engineers whose work in R & D or academia involves the practical consequences of chaotic dynamics.