Topics In Bifurcation Theory And Applications

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Topics in Bifurcation Theory and Applications

Author : Grard Iooss
Publisher : World Scientific
ISBN 13 : 9789810237288
Total Pages : 204 pages
Book Rating : 4.2/5 (372 download)

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Book Synopsis Topics in Bifurcation Theory and Applications by : Grard Iooss

Download or read book Topics in Bifurcation Theory and Applications written by Grard Iooss and published by World Scientific. This book was released on 1998 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Topics in Bifurcation Theory and Applications

Author : GÃ©rard Iooss
Publisher : World Scientific Publishing Company
ISBN 13 : 9813105348
Total Pages : 196 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Topics in Bifurcation Theory and Applications by : GÃ©rard Iooss

Download or read book Topics in Bifurcation Theory and Applications written by GÃ©rard Iooss and published by World Scientific Publishing Company. This book was released on 1999-01-22 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Elements of Applied Bifurcation Theory

Author : Yuri Kuznetsov
Publisher : Springer Science & Business Media
ISBN 13 : 1475739788
Total Pages : 648 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Elements of Applied Bifurcation Theory by : Yuri Kuznetsov

Download or read book Elements of Applied Bifurcation Theory written by Yuri Kuznetsov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Topics In Bifurcation Theory And Applications (2nd Edition)

Author : Moritz Adelmeyer
Publisher :
ISBN 13 : 9789812815729
Total Pages : 196 pages
Book Rating : 4.8/5 (157 download)

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Book Synopsis Topics In Bifurcation Theory And Applications (2nd Edition) by : Moritz Adelmeyer

Download or read book Topics In Bifurcation Theory And Applications (2nd Edition) written by Moritz Adelmeyer and published by . This book was released on 1999 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Bifurcation Theory And Applications

Author : Shouhong Wang
Publisher : World Scientific
ISBN 13 : 9814480592
Total Pages : 391 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Bifurcation Theory And Applications by : Shouhong Wang

Download or read book Bifurcation Theory And Applications written by Shouhong Wang and published by World Scientific. This book was released on 2005-06-27 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Topics in Stability and Bifurcation Theory

Author : David H. Sattinger
Publisher : Springer
ISBN 13 : 3540383336
Total Pages : 197 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Topics in Stability and Bifurcation Theory by : David H. Sattinger

Download or read book Topics in Stability and Bifurcation Theory written by David H. Sattinger and published by Springer. This book was released on 2006-11-15 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt:

topics in bifurcation theory and applications second edition.

Author :
Publisher : Allied Publishers
ISBN 13 : 9788177644609
Total Pages : 208 pages
Book Rating : 4.6/5 (446 download)

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Book Synopsis topics in bifurcation theory and applications second edition. by :

Download or read book topics in bifurcation theory and applications second edition. written by and published by Allied Publishers. This book was released on with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Singularities and Groups in Bifurcation Theory

Author : Martin Golubitsky
Publisher : Springer Science & Business Media
ISBN 13 : 146125034X
Total Pages : 480 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Singularities and Groups in Bifurcation Theory by : Martin Golubitsky

Download or read book Singularities and Groups in Bifurcation Theory written by Martin Golubitsky and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has been written in a frankly partisian spirit-we believe that singularity theory offers an extremely useful approach to bifurcation prob lems and we hope to convert the reader to this view. In this preface we will discuss what we feel are the strengths of the singularity theory approach. This discussion then Ieads naturally into a discussion of the contents of the book and the prerequisites for reading it. Let us emphasize that our principal contribution in this area has been to apply pre-existing techniques from singularity theory, especially unfolding theory and classification theory, to bifurcation problems. Many ofthe ideas in this part of singularity theory were originally proposed by Rene Thom; the subject was then developed rigorously by John Matherand extended by V. I. Arnold. In applying this material to bifurcation problems, we were greatly encouraged by how weil the mathematical ideas of singularity theory meshed with the questions addressed by bifurcation theory. Concerning our title, Singularities and Groups in Bifurcation Theory, it should be mentioned that the present text is the first volume in a two-volume sequence. In this volume our emphasis is on singularity theory, with group theory playing a subordinate role. In Volume II the emphasis will be more balanced. Having made these remarks, Iet us set the context for the discussion of the strengths of the singularity theory approach to bifurcation. As we use the term, bifurcation theory is the study of equations with multiple solutions.

Bifurcation Theory

Author : Hansjörg Kielhöfer
Publisher : Springer Science & Business Media
ISBN 13 : 0387216332
Total Pages : 355 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Bifurcation Theory by : Hansjörg Kielhöfer

Download or read book Bifurcation Theory written by Hansjörg Kielhöfer and published by Springer Science & Business Media. This book was released on 2006-04-10 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Global Bifurcation Theory and Hilbert’s Sixteenth Problem

Author : V. Gaiko
Publisher : Springer Science & Business Media
ISBN 13 : 1441991689
Total Pages : 199 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Global Bifurcation Theory and Hilbert’s Sixteenth Problem by : V. Gaiko

Download or read book Global Bifurcation Theory and Hilbert’s Sixteenth Problem written by V. Gaiko and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: On the 8th of August 1900 outstanding German mathematician David Hilbert delivered a talk "Mathematical problems" at the Second Interna tional Congress of Mathematicians in Paris. The talk covered practically all directions of mathematical thought of that time and contained a list of 23 problems which determined the further development of mathema tics in many respects (1, 119]. Hilbert's Sixteenth Problem (the second part) was stated as follows: Problem. To find the maximum number and to determine the relative position of limit cycles of the equation dy Qn(X, y) -= dx Pn(x, y)' where Pn and Qn are polynomials of real variables x, y with real coeffi cients and not greater than n degree. The study of limit cycles is an interesting and very difficult problem of the qualitative theory of differential equations. This theory was origi nated at the end of the nineteenth century in the works of two geniuses of the world science: of the Russian mathematician A. M. Lyapunov and of the French mathematician Henri Poincare. A. M. Lyapunov set forth and solved completely in the very wide class of cases a special problem of the qualitative theory: the problem of motion stability (154]. In turn, H. Poincare stated a general problem of the qualitative analysis which was formulated as follows: not integrating the differential equation and using only the properties of its right-hand sides, to give as more as possi ble complete information on the qualitative behaviour of integral curves defined by this equation (176].

Bifurcation: Analysis, Algorithms, Applications

Author : KÜPPER
Publisher : Birkhäuser
ISBN 13 : 3034872410
Total Pages : 368 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Bifurcation: Analysis, Algorithms, Applications by : KÜPPER

Download or read book Bifurcation: Analysis, Algorithms, Applications written by KÜPPER and published by Birkhäuser. This book was released on 2013-03-08 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: The conference on BIFURCATIONS: ANALYSIS, ALGORITHMS, APPLICATIONS took place in Dortmund in August 18 - 22, 1986. More then 150 Scientists from 16 countries participated in the meeting, among them mathematicians, engi neers, and physicists. A broad spectrum of new results on bifurcation was covered by 49 talks. The diversity of the range of treated topics and of involved fields inspired fruitful discussions. 36 refereed papers are contained in these proceedings. The subjects covered treat bifurcation problems, ranging from theoretical investigations to numerical results, with emphasis placed upon applications. The more theoreti cal papers include the topics symmetry breaking, delay differential equations, Cornu spirals, homoclinic orbits, and selfsimilarity. Different kinds of bifurcations are treated: Hopf bifurcation, bifurcation from continuous spec trum, complex bifurcation, and bifurcation near tori. Several numerical as pects are discussed, among them continuation, block elimination, and spectral methods. Algorithms are proposed for approximating manifolds, calculating pe riodic solutions and handling multi-parameter problems. Ample space is devoted to· applications. Classical phenomena from fluid mechanics (such as convection rolls and th~ Taylor vortex problem), buckling, and reaction-diffusion pro blems are considered. Other applications of bifurcations include railway vehicle dynamics, computer graphics, semiconductors, drilling processes, simu lation of oil reservoirs, and rotor dynamics. The proceedings reflect current research in bifurcation. They are an attempt to bring together researchers from differ~nt disciplines to stimulate common effort towards a better understanding and handling of bifurcation pro blems.

Dynamical Systems V

Author : V.I. Arnold
Publisher : Springer Science & Business Media
ISBN 13 : 3642578845
Total Pages : 279 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Dynamical Systems V by : V.I. Arnold

Download or read book Dynamical Systems V written by V.I. Arnold and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Bifurcation and Chaos

Author : Jan Awrejcewicz
Publisher : Springer
ISBN 13 :
Total Pages : 296 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Bifurcation and Chaos by : Jan Awrejcewicz

Download or read book Bifurcation and Chaos written by Jan Awrejcewicz and published by Springer. This book was released on 1995 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Elementary Stability and Bifurcation Theory

Author : Gerard Iooss
Publisher : Springer Science & Business Media
ISBN 13 : 1461209978
Total Pages : 347 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Elementary Stability and Bifurcation Theory by : Gerard Iooss

Download or read book Elementary Stability and Bifurcation Theory written by Gerard Iooss and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Bifurcation Theory of Functional Differential Equations

Author : Shangjiang Guo
Publisher : Springer Science & Business Media
ISBN 13 : 1461469929
Total Pages : 295 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Bifurcation Theory of Functional Differential Equations by : Shangjiang Guo

Download or read book Bifurcation Theory of Functional Differential Equations written by Shangjiang Guo and published by Springer Science & Business Media. This book was released on 2013-07-30 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).

Bifurcation Control

Author : Guanrong Chen
Publisher : Springer Science & Business Media
ISBN 13 : 9783540403418
Total Pages : 344 pages
Book Rating : 4.4/5 (34 download)

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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.

Methods of Bifurcation Theory

Author : S.-N. Chow
Publisher : Springer Science & Business Media
ISBN 13 : 1461381592
Total Pages : 529 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Methods of Bifurcation Theory by : S.-N. Chow

Download or read book Methods of Bifurcation Theory written by S.-N. Chow and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: An alternative title for this book would perhaps be Nonlinear Analysis, Bifurcation Theory and Differential Equations. Our primary objective is to discuss those aspects of bifurcation theory which are particularly meaningful to differential equations. To accomplish this objective and to make the book accessible to a wider we have presented in detail much of the relevant background audience, material from nonlinear functional analysis and the qualitative theory of differential equations. Since there is no good reference for some of the mate rial, its inclusion seemed necessary. Two distinct aspects of bifurcation theory are discussed-static and dynamic. Static bifurcation theory is concerned with the changes that occur in the structure of the set of zeros of a function as parameters in the function are varied. If the function is a gradient, then variational techniques play an important role and can be employed effectively even for global problems. If the function is not a gradient or if more detailed information is desired, the general theory is usually local. At the same time, the theory is constructive and valid when several independent parameters appear in the function. In differential equations, the equilibrium solutions are the zeros of the vector field. Therefore, methods in static bifurcation theory are directly applicable.