Practical Bifurcation and Stability Analysis, R?diger U. Seydel

Автор: Kuznetsov Yuri A.
Название: Elements of Applied Bifurcation Theory
ISBN: 0387219064 ISBN-13(EAN): 9780387219066
Издательство: Springer
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Описание: Explains the basic phenomena of bifurcation theory. This book provides a student or researcher with the basis in nonlinear dynamical systems and their bifurcations, giving them the necessary understanding of the approaches, methods, results and terminology used in the modern applied mathematics literature.

Автор: Seydel, Rudiger
Название: Practical bifurcation and stability analysis
ISBN: 144191739X ISBN-13(EAN): 9781441917393
Издательство: Springer
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Описание: 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.

Автор: Kielh?fer
Название: Bifurcation Theory
ISBN: 1461405017 ISBN-13(EAN): 9781461405016
Издательство: Springer
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Описание: 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. The second edition is substantially and formally revised and new material is added. Among this is bifurcation with a two-dimensional kernel with applications, the buckling of the Euler rod, the appearance of Taylor vortices, the singular limit process of the Cahn-Hilliard model, and an application of this method to more complicated nonconvex variational problems.  

Автор: Guo, Shangjiang, Wu, Jianhong
Название: Bifurcation Theory of Functional Differential Equations
ISBN: 1461469910 ISBN-13(EAN): 9781461469919
Издательство: Springer
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Описание: This book summarizes effective and general approaches and frameworks in the investigation of bifurcation phenomena for functional differential equations (FDEs). It provides all the tools from bifurcation theory and contains examples and applications.

Автор: Gerard Iooss; Daniel D. Joseph
Название: Elementary Stability and Bifurcation Theory
ISBN: 1461269776 ISBN-13(EAN): 9781461269779
Издательство: Springer
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Описание: In its most general form bifurcation theory is a theory of asymptotic solutions of nonlinear equations. By asymptotic solutions we mean, for example, steady solutions, time-periodic solutions, and quasi-periodic solutions. The purpose of this book is to teach the theory of bifurcation of asymptotic solutions of evolution problems governed by nonlinear differential equations. We have written this book for the broadest audience of potentially interested learners: engineers, biologists, chemists, physicists, mathematicians, economists, and others whose work involves understanding asymptotic solutions of nonlinear differential equations. To accomplish our aims, we have thought it necessary to make the analysis: (1) general enough to apply to the huge variety of applications which arise in science and technology; and (2) simple enough so that it can be understood by persons whose mathe- matical training does not extend beyond the classical methods of analysis which were popular in the nineteenth century. Of course, it is not possible to achieve generality and simplicity in a perfect union but, in fact, the general theory is simpler than the detailed theory required for particular applications. The general theory abstracts from the detailed problems only the essential features and provides the student with the skeleton on which detailed structures of the applications must rest. lt is generally believed that the mathematical theory of bifurcation requires some functional analysis and some ofthe methods of topology and dynamics.

Автор: K?PPER; SEYDEL; TROGER
Название: Bifurcation: Analysis, Algorithms, Applications
ISBN: 3034872437 ISBN-13(EAN): 9783034872430
Издательство: Springer
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Описание: The subjects covered treat bifurcation problems, ranging from theoretical investigations to numerical results, with emphasis placed upon applications. Different kinds of bifurcations are treated: Hopf bifurcation, bifurcation from continuous spec- trum, complex bifurcation, and bifurcation near tori.

Автор: Zhen Mei
Название: Numerical Bifurcation Analysis for Reaction-Diffusion Equations
ISBN: 3642086691 ISBN-13(EAN): 9783642086694
Издательство: Springer
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Описание: This monograph is the first to provide readers with numerical tools for a systematic analysis of bifurcation problems in reaction-diffusion equations. Readers will gain a thorough understanding of numerical bifurcation analysis and the necessary tools for investigating nonlinear phenomena in reaction-diffusion equations.

Автор: Kiyohiro Ikeda; Kazuo Murota
Название: Bifurcation Theory for Hexagonal Agglomeration in Economic Geography
ISBN: 4431563385 ISBN-13(EAN): 9784431563389
Издательство: Springer
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Описание: This book offers a theoretical foundation for the self-organization of hexagonal agglomeration patterns of industrial regions, surveying the bifurcations of economic geography models for a system of cities on a hexagonal lattice. Offers advice on application.

Автор: Gerard Iooss; Daniel D. Joseph
Название: Elementary Stability and Bifurcation Theory
ISBN: 0387970681 ISBN-13(EAN): 9780387970684
Издательство: Springer
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Цена: 68900.00 T
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Описание: In its most general form bifurcation theory is a theory of asymptotic solutions of nonlinear equations. By asymptotic solutions we mean, for example, steady solutions, time-periodic solutions, and quasi-periodic solutions. The purpose of this book is to teach the theory of bifurcation of asymptotic solutions of evolution problems governed by nonlinear differential equations. We have written this book for the broadest audience of potentially interested learners: engineers, biologists, chemists, physicists, mathematicians, economists, and others whose work involves understanding asymptotic solutions of nonlinear differential equations. To accomplish our aims, we have thought it necessary to make the analysis: (1) general enough to apply to the huge variety of applications which arise in science and technology; and (2) simple enough so that it can be understood by persons whose mathe- matical training does not extend beyond the classical methods of analysis which were popular in the nineteenth century. Of course, it is not possible to achieve generality and simplicity in a perfect union but, in fact, the general theory is simpler than the detailed theory required for particular applications. The general theory abstracts from the detailed problems only the essential features and provides the student with the skeleton on which detailed structures of the applications must rest. lt is generally believed that the mathematical theory of bifurcation requires some functional analysis and some ofthe methods of topology and dynamics.

Автор: David H. Sattinger
Название: Topics in Stability and Bifurcation Theory
ISBN: 3540061339 ISBN-13(EAN): 9783540061335
Издательство: Springer
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Автор: Hans Troger; Alois Steindl
Название: Nonlinear Stability and Bifurcation Theory
ISBN: 3211822925 ISBN-13(EAN): 9783211822920
Издательство: Springer
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Описание: Every student in engineering or in other fields of the applied sciences who has passed through his curriculum knows that the treatment of nonlin- ear problems has been either avoided completely or is confined to special courses where a great number of different ad-hoc methods are presented.

Автор: K?PPER; SCHNEIDER; SEYDEL; TROGER
Название: Bifurcation and Chaos: Analysis, Algorithms, Applications
ISBN: 303487006X ISBN-13(EAN): 9783034870061
Издательство: Springer
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Описание: This volume contains the proceedings of a conference held in Wiirzburg, August 20-24, 1990. How trends vary may be seen by comparing these proceedings with previous ones, in particular with the conference held in Dortmund 1986 (proceedings published in ISNM 79).