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Author: Martin Golubitsky Publisher: American Mathematical Soc. ISBN: 0821850601 Category : Mathematics Languages : en Pages : 408
Book Description
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.
Author: Martin Golubitsky Publisher: American Mathematical Soc. ISBN: 0821850601 Category : Mathematics Languages : en Pages : 408
Book Description
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.
Author: Martin Golubitsky Publisher: Springer Science & Business Media ISBN: 146125034X Category : Mathematics Languages : en Pages : 480
Book Description
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.
Author: Jorge L. Moiola Publisher: World Scientific ISBN: 9789810226282 Category : Mathematics Languages : en Pages : 354
Book Description
This book is devoted to the frequency domain approach, for both regular and degenerate Hopf bifurcation analyses. Besides showing that the time and frequency domain approaches are in fact equivalent, the fact that many significant results and computational formulas obtained in the studies of regular and degenerate Hopf bifurcations from the time domain approach can be translated and reformulated into the corresponding frequency domain setting, and be reconfirmed and rediscovered by using the frequency domain methods, is also explained. The description of how the frequency domain approach can be used to obtain several types of standard bifurcation conditions for general nonlinear dynamical systems is given as well as is demonstrated a very rich pictorial gallery of local bifurcation diagrams for nonlinear systems under simultaneous variations of several system parameters. In conjunction with this graphical analysis of local bifurcation diagrams, the defining and nondegeneracy conditions for several degenerate Hopf bifurcations is presented. With a great deal of algebraic computation, some higher-order harmonic balance approximation formulas are derived, for analyzing the dynamical behavior in small neighborhoods of certain types of degenerate Hopf bifurcations that involve multiple limit cycles and multiple limit points of periodic solutions. In addition, applications in chemical, mechanical and electrical engineering as well as in biology are discussed. This book is designed and written in a style of research monographs rather than classroom textbooks, so that the most recent contributions to the field can be included with references.
Author: Dingjun Luo Publisher: World Scientific ISBN: 9789810220945 Category : Science Languages : en Pages : 484
Book Description
Dynamical bifurcation theory is concerned with the changes that occur in the global structure of dynamical systems as parameters are varied. This book makes recent research in bifurcation theory of dynamical systems accessible to researchers interested in this subject. In particular, the relevant results obtained by Chinese mathematicians are introduced as well as some of the works of the authors which may not be widely known. The focus is on the analytic approach to the theory and methods of bifurcations. The book prepares graduate students for further study in this area, and it serves as a ready reference for researchers in nonlinear sciences and applied mathematics.
Author: Alexander P. Seyranian Publisher: World Scientific ISBN: 9812384065 Category : Technology & Engineering Languages : en Pages : 421
Book Description
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.
Author: Maoan Han Publisher: World Scientific ISBN: 9814501093 Category : Mathematics Languages : en Pages : 476
Book Description
Dynamical bifurcation theory is concerned with the changes that occur in the global structure of dynamical systems as parameters are varied. This book makes recent research in bifurcation theory of dynamical systems accessible to researchers interested in this subject. In particular, the relevant results obtained by Chinese mathematicians are introduced as well as some of the works of the authors which may not be widely known. The focus is on the analytic approach to the theory and methods of bifurcations. The book prepares graduate students for further study in this area, and it serves as a ready reference for researchers in nonlinear sciences and applied mathematics.
Author: Michiel Hazewinkel Publisher: Springer Science & Business Media ISBN: 9400962398 Category : Mathematics Languages : en Pages : 258
Book Description
Bifurcation theory has made a very fast upswing in the last fifteen years. Roughly speaking it generalises to dynamic systems the pos sibility of mUltiple solutions, a possibility already recognised in static systems - physical, chemical, social - when operating far from their equilibrium states. It so happened that quite a few staff members of the Erasmus University Rotterdam were thinking along those lines about certain aspects of their disciplines. To have a number of specialists and potential "fans" convene to discuss various aspects of bifurcation al thinking, seemed a natural development. The resulting papers were judged to be of interest to a larger public, and as such are logically regrouped in this volume, one in a series of studies resulting from the activities of the Steering Committee on Interdisciplinary Studies of the Erasmus University, Rotterdam. Although the volume is perhaps multidisciplinary rather than interdisciplinary - the interdisciplinary aspect being only "latent" -, as a "soft" interdisciplinary exercise (the application of formal structures of one discipline to another) it has a right to interdisciplinary existence! This book could not have been published without a generous grant of the University Foundation of the Erasmus University Rotterdam, which allowed the conference to be held and the resulting papers to be published; that generosity is gratefully acknowledged.
Author: Martin Golubitsky
Author: Martin Golubitsky
Author: John M. Guckenheimer
Author: Martin Golubitsky
Author: Jorge L. Moiola
Author: John M. Guckenheimer
Author: Dingjun Luo
Author: Mahmoud H. M. Sallam
Author: Alexander P. Seyranian
Author: Maoan Han
Author: Michiel Hazewinkel