Download or read book Global Bifurcation of Periodic Solutions with Symmetry written by Bernold Fiedler and published by Springer. This book was released on 2006-11-14 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: This largely self-contained research monograph addresses the following type of questions. Suppose one encounters a continuous time dynamical system with some built-in symmetry. Should one expect periodic motions which somehow reflect this symmetry? And how would periodicity harmonize with symmetry? Probing into these questions leads from dynamics to topology, algebra, singularity theory, and to many applications. Within a global approach, the emphasis is on periodic motions far from equilibrium. Mathematical methods include bifurcation theory, transversality theory, and generic approximations. A new homotopy invariant is designed to study the global interdependence of symmetric periodic motions. Besides mathematical techniques, the book contains 5 largely nontechnical chapters. The first three outline the main questions, results and methods. A detailed discussion pursues theoretical consequences and open problems. Results are illustrated by a variety of applications including coupled oscillators and rotating waves: these links to such disciplines as theoretical biology, chemistry, fluid dynamics, physics and their engineering counterparts make the book directly accessible to a wider audience.
Download or read book Global Bifurcations with Symmetry written by Jeffrey Brent Porter and published by . This book was released on 2001 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Analytic Theory of Global Bifurcation written by Boris Buffoni and published by Princeton University Press. This book was released on 2003-02-02 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher Description
Download or read book Global Bifurcations and Chaos written by Stephen Wiggins and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: Global Bifurcations and Chaos: Analytical Methods is unique in the literature of chaos in that it not only defines the concept of chaos in deterministic systems, but it describes the mechanisms which give rise to chaos (i.e., homoclinic and heteroclinic motions) and derives explicit techniques whereby these mechanisms can be detected in specific systems. These techniques can be viewed as generalizations of Melnikov's method to multi-degree of freedom systems subject to slowly varying parameters and quasiperiodic excitations. A unique feature of the book is that each theorem is illustrated with drawings that enable the reader to build visual pictures of global dynamcis of the systems being described. This approach leads to an enhanced intuitive understanding of the theory.
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).
Download or read book Bifurcation and Symmetry written by BÖHMER and published by Birkhäuser. This book was released on 2013-03-08 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symmetry is a property which occurs throughout nature and it is therefore natural that symmetry should be considered when attempting to model nature. In many cases, these models are also nonlinear and it is the study of nonlinear symmetric models that has been the basis of much recent work. Although systematic studies of nonlinear problems may be traced back at least to the pioneering contributions of Poincare, this remains an area with challenging problems for mathematicians and scientists. Phenomena whose models exhibit both symmetry and nonlinearity lead to problems which are challenging and rich in complexity, beauty and utility. In recent years, the tools provided by group theory and representation theory have proven to be highly effective in treating nonlinear problems involving symmetry. By these means, highly complex situations may be decomposed into a number of simpler ones which are already understood or are at least easier to handle. In the realm of numerical approximations, the systematic exploitation of symmetry via group repre sentation theory is even more recent. In the hope of stimulating interaction and acquaintance with results and problems in the various fields of applications, bifurcation theory and numerical analysis, we organized the conference and workshop Bifurcation and Symmetry: Cross Influences between Mathematics and Applications during June 2-7,8-14, 1991 at the Philipps University of Marburg, Germany.
Download or read book Bifurcation Symmetry and Patterns written by Jorge Buescu and published by Birkhäuser. This book was released on 2012-12-06 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: The latest developments on both the theory and applications of bifurcations with symmetry. The text includes recent experimental work as well as new approaches to and applications of the theory to other sciences. It shows the range of dissemination of the work of Martin Golubitsky and Ian Stewart and its influence in modern mathematics at the same time as it contains work of young mathematicians in new directions. The range of topics includes mathematical biology, pattern formation, ergodic theory, normal forms, one-dimensional dynamics and symmetric dynamics.
Download or read book Dynamics and Symmetry written by Mike Field and published by World Scientific. This book was released on 2007 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the first systematic exposition of the global and local theory of dynamics equivariant with respect to a (compact) Lie group. Aside from general genericity and normal form theorems on equivariant bifurcation, it describes many general families of examples of equivariant bifurcation and includes a number of novel geometric techniques, in particular, equivariant transversality. This important book forms a theoretical basis of future work on equivariant reversible and Hamiltonian systems.This book also provides a general and comprehensive introduction to codimension one equivariant bifurcation theory. In particular, it includes the bifurcation theory developed with Roger Richardson on subgroups of reflection groups and the Maximal Isotropy Subgroup Conjecture. A number of general results are also given on the global theory. Introductory material on groups, representations and G-manifolds are covered in the first three chapters of the book. In addition, a self-contained introduction of equivariant transversality is given, including necessary results on stratifications as well as results on equivariant jet transversality developed by Edward Bierstone.
Download or read book Lectures on Bifurcations Dynamics and Symmetry written by Michael Field and published by CRC Press. This book was released on 1996-09-11 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an expanded version of a Master Class on the symmetric bifurcation theory of differential equations given by the author at the University of Twente in 1995. The notes cover a wide range of recent results in the subject, and focus on the dynamics that can appear in the generic bifurcation theory of symmetric differential equations. Many of the results and examples in the book are new and have not been previously published. The first four chapters contain an accessible presentation of the fundamental work by Field and Richardson on symmetry breaking and the Maximal Isotropy Subgroup Conjecture. The remainder of the book focuses on recent research of the author and includes chapters on the invariant sphere theorem, coupled cell systems, heteroclinic cycles , equivariant transversality, and an Appendix (with Xiaolin Peng) giving a new low dimensional counterexample to the converse of the Maximal Isotropy Subgroup Conjecture. The chapter on coupled cell systems includes a weath of new examples of 'cycling chaos'. The chapter on equivariant transversality is introductory and centres on an extended discussion of an explicit system of four coupled nonlinear oscillators. The style and format of the original lectures has largely been maintained and the notes include over seventy exercises *with hints for solutions and suggestions kfor further reading). In general terms, the notes are directed at mathematicians and aplied scientists working in the field of bifurcation theory who wish to learn about some of the latest developments and techniques in equivariant bifurcation theory. The notes are relatively self-contained and are structured so that they can form the basis for a graduate level course in equivariant bifurcation theory.
Download or read book Dynamical Symmetry written by Carl Wulfman and published by World Scientific. This book was released on 2011 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: Whenever systems are governed by continuous chains of causes and effects, their behavior exhibits the consequences of dynamical symmetries, many of them far from obvious. Dynamical Symmetry introduces the reader to Sophus Lie's discoveries of the connections between differential equations and continuous groups that underlie this observation. It develops and applies the mathematical relations between dynamics and geometry that result. Systematic methods for uncovering dynamical symmetries are described, and put to use. Much material in the book is new and some has only recently appeared in research journals. Though Lie groups play a key role in elementary particle physics, their connection with differential equations is more often exploited in applied mathematics and engineering. Dynamical Symmetry bridges this gap in a novel manner designed to help readers establish new connections in their own areas of interest. Emphasis is placed on applications to physics and chemistry. Applications to many of the other sciences illustrate both general principles and the ubiquitousness of dynamical symmetries.
Download or read book Local Bifurcations Center Manifolds and Normal Forms in Infinite Dimensional Dynamical Systems written by Mariana Haragus and published by Springer Science & Business Media. This book was released on 2010-11-23 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: An extension of different lectures given by the authors, Local Bifurcations, Center Manifolds, and Normal Forms in Infinite Dimensional Dynamical Systems provides the reader with a comprehensive overview of these topics. Starting with the simplest bifurcation problems arising for ordinary differential equations in one- and two-dimensions, this book describes several tools from the theory of infinite dimensional dynamical systems, allowing the reader to treat more complicated bifurcation problems, such as bifurcations arising in partial differential equations. Attention is restricted to the study of local bifurcations with a focus upon the center manifold reduction and the normal form theory; two methods that have been widely used during the last decades. Through use of step-by-step examples and exercises, a number of possible applications are illustrated, and allow the less familiar reader to use this reduction method by checking some clear assumptions. Written by recognised experts in the field of center manifold and normal form theory this book provides a much-needed graduate level text on bifurcation theory, center manifolds and normal form theory. It will appeal to graduate students and researchers working in dynamical system theory.
Download or read book Bifurcations and Symmetry in Dissipative Dynamics written by Philip Conway Hirschberg and published by . This book was released on 1994 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Symmetry Perspective written by Martin Golubitsky and published by Birkhäuser. This book was released on 2012-12-06 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: The framework of ‘symmetry’ provides an important route between the abstract theory and experimental observations. The book applies symmetry methods to dynamical systems, focusing on bifurcation and chaos theory. Its exposition is organized around a wide variety of relevant applications. From the reviews: "[The] rich collection of examples makes the book...extremely useful for motivation and for spreading the ideas to a large Community."--MATHEMATICAL REVIEWS
Download or read book Dynamics Bifurcation and Symmetry written by Pascal Chossat and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects contributions to the conference" Dynamics, Bifurcation and Symmetry, new trends and new tools", which was held at the Institut d'Etudes Sci entifiques de Cargese (France), September 3-9, 1993. The first aim of this conference was to gather and summarize the work of the European Bifurcation Theory Group after two years of existence (the EBTG links european laboratories in five countries via an EC grant). Thanks to a NATO ARW grant, the conference developed into an international meeting on bifurcation theory and dynamical systems, with the partic ipation of leading specialists not only from Europe but also from overseas countries (Canada, USA, South America). It was a great satisfaction to notice the active, and quite enthusiastic participation of many young scientists. This is reflected in the present book for which many contributors are PhD students or post-doc researchers. Although several "big" themes (bifurcation with symmetry, low dimensional dynam ics, dynamics in EDP's, applications, . . . ) are present in these proceedings, we have divided the book into corresponding parts. In fact these themes overlap in most contributions, which seems to reflect a general tendancy in nonlinear science. I am very pleased to thank for their support the NATO International Exchange Scientific Program as well as the EEC Science Program, which made possible the suc cess of this conference.
Download or read book Symmetry Nonlinear Bifurcation Analysis and Parallel Computation written by James Christopher Wohlever and published by . This book was released on 1996 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Numerical Continuation and Bifurcation in Nonlinear PDEs written by Hannes Uecker and published by SIAM. This book was released on 2021-08-19 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a hands-on approach to numerical continuation and bifurcation for nonlinear PDEs in 1D, 2D, and 3D. Partial differential equations (PDEs) are the main tool to describe spatially and temporally extended systems in nature. PDEs usually come with parameters, and the study of the parameter dependence of their solutions is an important task. Letting one parameter vary typically yields a branch of solutions, and at special parameter values, new branches may bifurcate. After a concise review of some analytical background and numerical methods, the author explains the free MATLAB package pde2path by using a large variety of examples with demo codes that can be easily adapted to the reader's given problem. Numerical Continuation and Bifurcation in Nonlinear PDEs will appeal to applied mathematicians and scientists from physics, chemistry, biology, and economics interested in the numerical solution of nonlinear PDEs, particularly the parameter dependence of solutions. It can be used as a supplemental text in courses on nonlinear PDEs and modeling and bifurcation.
