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Author :
Publisher :
ISBN 13 :
Total Pages : 240 pages
Book Rating : 4.:/5 (44 download)
Download or read book Bifurcation, théorie ergodique et applications written by and published by . This book was released on 1982 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jorge Buescu
Publisher : Birkhäuser
ISBN 13 : 3034879822
Total Pages : 215 pages
Book Rating : 4.0/5 (348 download)
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.
Author :
Publisher :
ISBN 13 : 9781468493801
Total Pages : pages
Book Rating : 4.4/5 (938 download)
Download or read book Bifurcation Theory written by and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Hansjörg Kielhöfer
Publisher : Springer Science & Business Media
ISBN 13 : 1461405025
Total Pages : 406 pages
Book Rating : 4.4/5 (614 download)
Download or read book Bifurcation Theory written by Hansjörg Kielhöfer and published by Springer Science & Business Media. This book was released on 2011-11-13 with total page 406 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. 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.
Author : Grard Iooss
Publisher : World Scientific
ISBN 13 : 9789810237288
Total Pages : 204 pages
Book Rating : 4.2/5 (372 download)
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.
Author : Tian Ma
Publisher : World Scientific
ISBN 13 : 9812562877
Total Pages : 392 pages
Book Rating : 4.8/5 (125 download)
Download or read book Bifurcation Theory and Applications written by Tian Ma and published by World Scientific. This book was released on 2005 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: - Provides a comprehensive and intuitive review of existing bifurcation theories - New theories for bifurcations from eigenvalues with even multiplicity - General recipes for applications
Author : Pascal Chossat
Publisher : World Scientific Publishing Company
ISBN 13 : 9813105445
Total Pages : 422 pages
Book Rating : 4.8/5 (131 download)
Download or read book Methods In Equivariant Bifurcations And Dynamical Systems written by Pascal Chossat and published by World Scientific Publishing Company. This book was released on 2000-02-28 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book presents a comprehensive introduction to bifurcation theory in the presence of symmetry, an applied mathematical topic which has developed considerably over the past twenty years and has been very successful in analysing and predicting pattern formation and other critical phenomena in most areas of science where nonlinear models are involved, like fluid flow instabilities, chemical waves, elasticity and population dynamics.The book has two aims. One is to expound the mathematical methods of equivariant bifurcation theory. Beyond the classical bifurcation tools, such as center manifold and normal form reductions, the presence of symmetry requires the introduction of the algebraic and geometric formalism of Lie group theory and transformation group methods. For the first time, all these methods in equivariant bifurcations are presented in a coherent and self-consistent way in a book.The other aim is to present the most recent ideas and results in this theory, in relation to applications. This includes bifurcations of relative equilibria and relative periodic orbits for compact and noncompact group actions, heteroclinic cycles and forced symmetry-breaking perturbations. Although not all recent contributions could be included and a choice had to be made, a rather complete description of these new developments is provided. At the end of every chapter, exercises are offered to the reader.
Author : Michal Fečkan
Publisher : Springer Science & Business Media
ISBN 13 : 1402087241
Total Pages : 266 pages
Book Rating : 4.4/5 (2 download)
Download or read book Topological Degree Approach to Bifurcation Problems written by Michal Fečkan and published by Springer Science & Business Media. This book was released on 2008-06-29 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. 1 Preface Many phenomena from physics, biology, chemistry and economics are modeled by di?erential equations with parameters. When a nonlinear equation is est- lished, its behavior/dynamics should be understood. In general, it is impossible to ?nd a complete dynamics of a nonlinear di?erential equation. Hence at least, either periodic or irregular/chaotic solutions are tried to be shown. So a pr- erty of a desired solution of a nonlinear equation is given as a parameterized boundary value problem. Consequently, the task is transformed to a solvability of an abstract nonlinear equation with parameters on a certain functional space. When a family of solutions of the abstract equation is known for some para- ters, the persistence or bifurcations of solutions from that family is studied as parameters are changing. There are several approaches to handle such nonl- ear bifurcation problems. One of them is a topological degree method, which is rather powerful in cases when nonlinearities are not enough smooth. The aim of this book is to present several original bifurcation results achieved by the author using the topological degree theory. The scope of the results is rather broad from showing periodic and chaotic behavior of non-smooth mechanical systems through the existence of traveling waves for ordinary di?erential eq- tions on in?nite lattices up to study periodic oscillations of undamped abstract waveequationsonHilbertspaceswithapplicationstononlinearbeamandstring partial di?erential equations. 1.
Author : Hendrik Wolter Broer
Publisher : American Mathematical Soc.
ISBN 13 : 082182483X
Total Pages : 189 pages
Book Rating : 4.8/5 (218 download)
Download or read book Unfoldings and Bifurcations of Quasi-Periodic Tori written by Hendrik Wolter Broer and published by American Mathematical Soc.. This book was released on 1990 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part I. We consider dynamical systems depending on parameters in various, both conservative and dissipative settings. For such systems integrability is defined as equivariance with respect to an appropriate torus action.
Author : Stefan Liebscher
Publisher : Springer
ISBN 13 : 3319107771
Total Pages : 144 pages
Book Rating : 4.3/5 (191 download)
Download or read book Bifurcation without Parameters written by Stefan Liebscher and published by Springer. This book was released on 2014-11-08 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: Targeted at mathematicians having at least a basic familiarity with classical bifurcation theory, this monograph provides a systematic classification and analysis of bifurcations without parameters in dynamical systems. Although the methods and concepts are briefly introduced, a prior knowledge of center-manifold reductions and normal-form calculations will help the reader to appreciate the presentation. Bifurcations without parameters occur along manifolds of equilibria, at points where normal hyperbolicity of the manifold is violated. The general theory, illustrated by many applications, aims at a geometric understanding of the local dynamics near the bifurcation points.
Author : Yuri A. Kuznetsov
Publisher : Springer Nature
ISBN 13 : 3031220072
Total Pages : 722 pages
Book Rating : 4.0/5 (312 download)
Download or read book Elements of Applied Bifurcation Theory written by Yuri A. Kuznetsov and published by Springer Nature. This book was released on 2023-04-18 with total page 722 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.
Author : Kevin E.M. Church
Publisher : Springer Nature
ISBN 13 : 3030645339
Total Pages : 388 pages
Book Rating : 4.0/5 (36 download)
Download or read book Bifurcation Theory of Impulsive Dynamical Systems written by Kevin E.M. Church and published by Springer Nature. This book was released on 2021-03-24 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents the most recent progress in bifurcation theory of impulsive dynamical systems with time delays and other functional dependence. It covers not only smooth local bifurcations, but also some non-smooth bifurcation phenomena that are unique to impulsive dynamical systems. The monograph is split into four distinct parts, independently addressing both finite and infinite-dimensional dynamical systems before discussing their applications. The primary contributions are a rigorous nonautonomous dynamical systems framework and analysis of nonlinear systems, stability, and invariant manifold theory. Special attention is paid to the centre manifold and associated reduction principle, as these are essential to the local bifurcation theory. Specifying to periodic systems, the Floquet theory is extended to impulsive functional differential equations, and this permits an exploration of the impulsive analogues of saddle-node, transcritical, pitchfork and Hopf bifurcations. Readers will learn how techniques of classical bifurcation theory extend to impulsive functional differential equations and, as a special case, impulsive differential equations without delays. They will learn about stability for fixed points, periodic orbits and complete bounded trajectories, and how the linearization of the dynamical system allows for a suitable definition of hyperbolicity. They will see how to complete a centre manifold reduction and analyze a bifurcation at a nonhyperbolic steady state.
Author : Visarath In
Publisher : Springer
ISBN 13 : 366255545X
Total Pages : 415 pages
Book Rating : 4.6/5 (625 download)
Download or read book Symmetry in Complex Network Systems written by Visarath In and published by Springer. This book was released on 2017-09-05 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book bridges the current gap between the theory of symmetry-based dynamics and its application to model and analyze complex systems. As an alternative approach, the authors use the symmetry of the system directly to formulate the appropriate models, and also to analyze the dynamics. Complex systems with symmetry arise in a wide variety of fields, including communication networks, molecular dynamics, manufacturing businesses, ecosystems, underwater vehicle dynamics, celestial and spacecraft dynamics and continuum mechanics. A general approach for their analysis has been to derive a detailed model of their individual parts, connect the parts and note that the system contains some sort of symmetry, then attempt to exploit this symmetry in order to simplify numerical computations. This approach can result in highly complicated models that are difficult to analyze even numerically. The alternative approach, while nonstandard, is not entirely new among the mathematics community. However, there is much less familiarity with the techniques of symmetry-breaking bifurcation, as they apply to the engineering, design and fabrication, of complex systems, in particular, nonlinear sensor devices with special emphasis on the conceptualization and development of new technologies of magnetic sensors such as fluxgate magnetometers and SQUID (Superconducting Quantum Interference Devices), E-- (electric-field) sensors, and communication and navigation systems that require multiple frequencies of operation, such as radar and antenna devices as well as gyroscopic systems.
Author : Kiyohiro Ikeda
Publisher : Springer Nature
ISBN 13 : 3030214737
Total Pages : 590 pages
Book Rating : 4.0/5 (32 download)
Download or read book Imperfect Bifurcation in Structures and Materials written by Kiyohiro Ikeda and published by Springer Nature. This book was released on 2019-09-25 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most physical systems lose or gain stability through bifurcation behavior. This book explains a series of experimentally found bifurcation phenomena by means of the methods of static bifurcation theory.
Author : Marat Akhmet
Publisher : Springer
ISBN 13 : 9811031800
Total Pages : 175 pages
Book Rating : 4.8/5 (11 download)
Download or read book Bifurcation in Autonomous and Nonautonomous Differential Equations with Discontinuities written by Marat Akhmet and published by Springer. This book was released on 2017-01-23 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on bifurcation theory for autonomous and nonautonomous differential equations with discontinuities of different types – those with jumps present either in the right-hand side, or in trajectories or in the arguments of solutions of equations. The results obtained can be applied to various fields, such as neural networks, brain dynamics, mechanical systems, weather phenomena and population dynamics. Developing bifurcation theory for various types of differential equations, the book is pioneering in the field. It presents the latest results and provides a practical guide to applying the theory to differential equations with various types of discontinuity. Moreover, it offers new ways to analyze nonautonomous bifurcation scenarios in these equations. As such, it shows undergraduate and graduate students how bifurcation theory can be developed not only for discrete and continuous systems, but also for those that combine these systems in very different ways. At the same time, it offers specialists several powerful instruments developed for the theory of discontinuous dynamical systems with variable moments of impact, differential equations with piecewise constant arguments of generalized type and Filippov systems.
Author : Yuri Kuznetsov
Publisher : Springer Science & Business Media
ISBN 13 : 1475739788
Total Pages : 648 pages
Book Rating : 4.4/5 (757 download)
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.
Author : Michal Fečkan
Publisher : Springer Science & Business Media
ISBN 13 : 3642182690
Total Pages : 387 pages
Book Rating : 4.6/5 (421 download)
Download or read book Bifurcation and Chaos in Discontinuous and Continuous Systems written by Michal Fečkan and published by Springer Science & Business Media. This book was released on 2011-05-30 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Bifurcation and Chaos in Discontinuous and Continuous Systems" provides rigorous mathematical functional-analytical tools for handling chaotic bifurcations along with precise and complete proofs together with concrete applications presented by many stimulating and illustrating examples. A broad variety of nonlinear problems are studied involving difference equations, ordinary and partial differential equations, differential equations with impulses, piecewise smooth differential equations, differential and difference inclusions, and differential equations on infinite lattices as well. This book is intended for mathematicians, physicists, theoretically inclined engineers and postgraduate students either studying oscillations of nonlinear mechanical systems or investigating vibrations of strings and beams, and electrical circuits by applying the modern theory of bifurcation methods in dynamical systems. Dr. Michal Fečkan is a Professor at the Department of Mathematical Analysis and Numerical Mathematics on the Faculty of Mathematics, Physics and Informatics at the Comenius University in Bratislava, Slovakia. He is working on nonlinear functional analysis, bifurcation theory and dynamical systems with applications to mechanics and vibrations.
