Multiparameter Bifurcation Theory
Multiparameter Bifurcation Theory

Author: Martin Golubitsky

Publisher: American Mathematical Soc.

Published: 1986

Total Pages: 408

ISBN-13: 0821850601

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This 1985 AMS Summer Research Conference brought together mathematicians interested in multiparameter bifurcation with scientists working on fluid instabilities and chemical reactor dynamics. This proceedings volume demonstrates the mutually beneficial interactions between the mathematical analysis, based on genericity, and experimental studies in these fields. Various papers study steady state bifurcation, Hopf bifurcation to periodic solutions, interactions between modes, dynamic bifurcations, and the role of symmetries in such systems. A section of abstracts at the end of the volume provides guides and pointers to the literature. The mathematical study of multiparameter bifurcation leads to a number of theoretical and practical difficulties, many of which are discussed in these papers. The articles also describe theoretical and experimental studies of chemical reactors, which provide many situations in which to test the mathematical ideas. Other test areas are found in fluid dynamics, particularly in studying the routes to chaos in two laboratory systems, Taylor-Couette flow between rotating cylinders and Rayleigh-Benard convection in a fluid layer.

Multiparameter Stability Theory with Mechanical Applications
Multiparameter Stability Theory with Mechanical Applications

Author: Alexander P. Seyranian

Publisher: World Scientific

Published: 2003

Total Pages: 421

ISBN-13: 9812384065

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This book deals with fundamental problems, concepts, and methods of multiparameter stability theory with applications in mechanics. It presents recent achievements and knowledge of bifurcation theory, sensitivity analysis of stability characteristics, general aspects of nonconservative stability problems, analysis of singularities of boundaries for the stability domains, stability analysis of multiparameter linear periodic systems, and optimization of structures under stability constraints. Systems with finite degrees of freedom and with continuous models are both considered. The book combines mathematical foundation with interesting classical and modern mechanical problems.A number of mechanical problems illustrating how bifurcations and singularities change the behavior of systems and lead to new physical phenomena are discussed. Among these problems, the authors consider systems of rotating bodies, tubes conveying fluid, elastic columns under the action of periodic and follower forces, optimization problems for conservative systems, etc. The methods presented are constructive and easy to implement in computer programs.This book is addressed to graduate students, academics, researchers, and practitioners in aerospace, naval, civil, and mechanical engineering. No special background is needed; just a basic knowledge of mathematics and mechanics.

Singularities and Groups in Bifurcation Theory
Singularities and Groups in Bifurcation Theory

Author: Martin Golubitsky

Publisher: Springer Science & Business Media

Published: 2013-11-27

Total Pages: 480

ISBN-13: 146125034X

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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 of Functional Differential Equations
Bifurcation Theory of Functional Differential Equations

Author: Shangjiang Guo

Publisher: Springer Science & Business Media

Published: 2013-07-30

Total Pages: 295

ISBN-13: 1461469929

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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).

Multiparameter Stability Theory with Mechanical Applications
Multiparameter Stability Theory with Mechanical Applications

Author: Alexander P. Seyranian

Publisher: World Scientific

Published: 2003

Total Pages: 428

ISBN-13: 9789812564443

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This book deals with fundamental problems, concepts, and methods ofmultiparameter stability theory with applications in mechanics. Itpresents recent achievements and knowledge of bifurcation theory, sensitivity analysis of stability characteristics, general aspects ofnonconservative stability problems, analysis of singularities ofboundaries for the stability domains, stability analysis ofmultiparameter linear periodic systems, and optimization of structuresunder stability constraints

Bifurcation Theory
Bifurcation Theory

Author: Hansjörg Kielhöfer

Publisher: Springer Science & Business Media

Published: 2011-11-13

Total Pages: 406

ISBN-13: 1461405025

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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.

Dynamics Reported
Dynamics Reported

Author:

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 258

ISBN-13: 3642612431

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Dynamics Reported is a series of books dedicated to the exposition of the mathematics of dynamcial systems. Its aim is to make the recent research accessible to advanced students and younger researchers. The series is also a medium for mathematicians to use to keep up-to-date with the work being done in neighboring fields. The style is best described as expository, but complete. Thus, there is an emphasis on examples and explanations, but also theorems normally occur with their proofs. The focus is on the analytic approach to dynamical systems, emphasizing the origins of the subject in the theory of differential equations. Dynamics Reported provides an excellent foundation for seminars on dynamical systems.

Stability Assessment of Power Systems with Multiple Voltage Source Converters
Stability Assessment of Power Systems with Multiple Voltage Source Converters

Author: Youhong Chen

Publisher: Springer Nature

Published: 2024

Total Pages: 247

ISBN-13: 3031630955

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This book offers a comprehensive assessment of the stability of modern power systems through advanced nonlinear analysis frameworks. It addresses the new challenges to power system stability posed by the anticipated integration of numerous power-electronic-interfaced devices needed to support renewable energy generation. Given the diverse operational timescales associated with controllers for power-electronic-interfaced devices, these devices can have an impact on a wide range of dynamic phenomena, thereby significantly influencing the system's dynamic performance and stability. The methodologies presented effectively manage the significant changes in system dynamics introduced by these devices. This research utilizes nonlinear methodologies, specifically bifurcation theory, to analyse various stability types in such power-electronic-rich systems. The book adopts a bifurcation-based methodology to evaluate power system stability through detailed examination of each type of instability mechanism. The methodology developed is extended to explore the interactions between multiple types of system stability considering the impacts of different voltage-source-converter controllers and grid strengths. Finally, to reduce the high computational burden imposed by the proposed methodology, a hybrid network model is developed to assess the system stability efficiently. Stability Assessment of Power Systems with Multiple Voltage Source Converters is of interest to students, researchers, and industry professionals in the field of electrical engineering.

Handbook of Differential Equations: Ordinary Differential Equations
Handbook of Differential Equations: Ordinary Differential Equations

Author: Flaviano Battelli

Publisher: Elsevier

Published: 2008-08-19

Total Pages: 719

ISBN-13: 0080559468

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This handbook is the fourth volume in a series of volumes devoted to self-contained and up-to-date surveys in the theory of ordinary differential equations, with an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wider audience. - Covers a variety of problems in ordinary differential equations - Pure mathematical and real-world applications - Written for mathematicians and scientists of many related fields