Download or read book Theory and Applications of Hopf Bifurcation written by B. D. Hassard and published by CUP Archive. This book was released on 1981-02-27 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text will be of value to all those interested in and studying the subject in the mathematical, natural and engineering sciences.
Download or read book The Hopf Bifurcation and Its Applications written by J. E. Marsden and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of these notes is to give a reasonahly com plete, although not exhaustive, discussion of what is commonly referred to as the Hopf bifurcation with applications to spe cific problems, including stability calculations. Historical ly, the subject had its origins in the works of Poincare [1] around 1892 and was extensively discussed by Andronov and Witt [1] and their co-workers starting around 1930. Hopf's basic paper [1] appeared in 1942. Although the term "Poincare Andronov-Hopf bifurcation" is more accurate (sometimes Friedrichs is also included), the name "Hopf Bifurcation" seems more common, so we have used it. Hopf's crucial contribution was the extension from two dimensions to higher dimensions. The principal technique employed in the body of the text is that of invariant manifolds. The method of Ruelle Takens [1] is followed, with details, examples and proofs added. Several parts of the exposition in the main text come from papers of P. Chernoff, J. Dorroh, O. Lanford and F. Weissler to whom we are grateful. The general method of invariant manifolds is common in dynamical systems and in ordinary differential equations: see for example, Hale [1,2] and Hartman [1]. Of course, other methods are also available. In an attempt to keep the picture balanced, we have included samples of alternative approaches. Specifically, we have included a translation (by L. Howard and N. Kopell) of Hopf's original (and generally unavailable) paper.
Download or read book Theory and Applications of Hopf Bifurcation written by B. D. Hassard and published by . This book was released on 1981 with total page 0 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 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.
Download or read book Hopf Bifurcation Analysis written by Jorge L. Moiola and published by World Scientific. This book was released on 1996 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Download or read book Bifurcation Theory written by Hansjörg Kielhöfer and published by Springer Science & Business Media. This book was released on 2006-04-10 with total page 355 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.
Download or read book Bifurcation and Chaos written by Jan Awrejcewicz and published by Springer. This book was released on 1995 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bifurcation and Chaos presents a collection of especially written articles describing the theory and application of nonlinear dynamics to a wide variety of problems encountered in physics and engineering. Each chapter is self-contained and includes an elementary introduction, an exposition of the present state of the art, and details of recent theoretical, computational and experimental results. Included among the practical systems analysed are: hysteretic circuits, Josephson circuits, magnetic systems, railway dynamics, rotor dynamics and nonlinear dynamics of speech. This book contains important information and ideas for all mathematicians, physicists and engineers whose work in R & D or academia involves the practical consequences of chaotic dynamics.
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 Introduction to Perturbation Methods written by Mark H. Holmes and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory graduate text is based on a graduate course the author has taught repeatedly over the last ten years to students in applied mathematics, engineering sciences, and physics. Each chapter begins with an introductory development involving ordinary differential equations, and goes on to cover such traditional topics as boundary layers and multiple scales. However, it also contains material arising from current research interest, including homogenisation, slender body theory, symbolic computing, and discrete equations. Many of the excellent exercises are derived from problems of up-to-date research and are drawn from a wide range of application areas.
Download or read book Delay Differential Equations and Applications written by O. Arino and published by Springer Science & Business Media. This book was released on 2006-09-25 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book groups material that was used for the Marrakech 2002 School on Delay Di'erential Equations and Applications. The school was held from September 9-21 2002 at the Semlalia College of Sciences of the Cadi Ayyad University, Marrakech, Morocco. 47 participants and 15 instructors originating from 21 countries attended the school. Fin- cial limitations only allowed support for part of the people from Africa andAsiawhohadexpressedtheirinterestintheschoolandhadhopedto come. Theschoolwassupportedby'nancementsfromNATO-ASI(Nato advanced School), the International Centre of Pure and Applied Mat- matics (CIMPA, Nice, France) and Cadi Ayyad University. The activity of the school consisted in courses, plenary lectures (3) and communi- tions (9), from Monday through Friday, 8. 30 am to 6. 30 pm. Courses were divided into units of 45mn duration, taught by block of two units, with a short 5mn break between two units within a block, and a 25mn break between two blocks. The school was intended for mathematicians willing to acquire some familiarity with delay di'erential equations or enhance their knowledge on this subject. The aim was indeed to extend the basic set of knowledge, including ordinary di'erential equations and semilinearevolutionequations,suchasforexamplethedi'usion-reaction equations arising in morphogenesis or the Belouzov-Zhabotinsky ch- ical reaction, and the classic approach for the resolution of these eq- tions by perturbation, to equations having in addition terms involving past values of the solution.
Download or read book Nonlinear Dynamical Economics and Chaotic Motion written by Hans-Walter Lorenz and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: The plan to publish the present book arose while I was preparing a joint work with Gunter Gabisch (Gabisch, G. /Lorenz, H. -W. : Business Cycle Theory. Berlin-Heidel berg-New York: Springer). It turned out that a lot of interesting material could only be sketched in a business cycle text, either because the relevance for business cycle theory was not evident or because the material required an interest in dynamical economics which laid beyond the scope of a survey text for advanced undergraduates. While much of the material enclosed in this book can be found in condensed and sometimes more or less identical form in that business cycle text, the present monograph attempts to present nonlinear dynamical economics in a broader context with economic examples from other fields than business cycle theory. It is a pleasure for me to acknowledge the critical comments, extremely detailed remarks, or suggestions by many friends and colleagues. The responses to earlier versions of the manuscript by W. A. Barnett, M. Boldrin, W. A. Brock, C. Chiarella, C. Dale, G. Feichtinger, P. Flaschel, D. K. Foley, R. M. Goodwin, D. Kelsey, M. Lines, A. Medio, L. Montrucchio, P. Read, C. Sayers, A. Schmutzler, H. Schnabl, G. Silverberg, H. -\'\!. Sinn, J. Sterman, and R. Tscherning not only encouraged me to publish the book in its present form but helped to remove numerous errors (not only typographic ones) and conceptnal misunderstandings and flaws. Particular thanks go to G.
Download or read book Frequency domain Approach To Hopf Bifurcation Analysis Continuous Time delayed Systems written by Franco Sebastian Gentile and published by World Scientific. This book was released on 2019-10-07 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the study of an effective frequency-domain approach, based on systems control theory, to compute and analyze several types of standard bifurcation conditions for general continuous-time nonlinear dynamical systems. A very rich pictorial gallery of local bifurcation diagrams for such nonlinear systems under simultaneous variations of several system parameters is presented. Some higher-order harmonic balance approximation formulas are derived for analyzing the oscillatory dynamics in small neighborhoods of certain types of Hopf and degenerate Hopf bifurcations.The frequency-domain approach is then extended to the large class of delay-differential equations, where the time delays can be either discrete or distributed. For the case of discrete delays, two alternatives are presented, depending on the structure of the underlying dynamical system, where the more general setting is then extended to the case of distributed time-delayed systems. Some representative examples in engineering and biology are discussed.
Download or read book Dynamics and Bifurcation in Networks written by Martin Golubitsky and published by SIAM. This book was released on 2023-04-24 with total page 867 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, there has been an explosion of interest in network-based modeling in many branches of science. This book synthesizes some of the common features of many such models, providing a general framework analogous to the modern theory of nonlinear dynamical systems. How networks lead to behavior not typical in a general dynamical system and how the architecture and symmetry of the network influence this behavior are the book’s main themes. Dynamics and Bifurcation in Networks: Theory and Applications of Coupled Differential Equations is the first book to describe the formalism for network dynamics developed over the past 20 years. In it, the authors introduce a definition of a network and the associated class of “admissible” ordinary differential equations, in terms of a directed graph whose nodes represent component dynamical systems and whose arrows represent couplings between these systems. They also develop connections between network architecture and the typical dynamics and bifurcations of these equations and discuss applications of this formalism to various areas of science, including gene regulatory networks, animal locomotion, decision-making, homeostasis, binocular rivalry, and visual illusions. This book will be of interest to scientific researchers in any area that uses network models, which includes many parts of biology, physics, chemistry, computer science, electrical and electronic engineering, psychology, and sociology.
Download or read book Topics in Bifurcation Theory and Applications written by Gérard Iooss and published by World Scientific Publishing Company. This book was released on 1999-01-22 with total page 196 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.
Download or read book The Hopf Bifurcation and Its Applications written by J. E Marsden and published by . This book was released on 1976-08-17 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt:
