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Author : Hans-Otto Walther
Publisher :
ISBN 13 :
Total Pages : 84 pages
Book Rating : 4.3/5 (121 download)
Download or read book Bifurcation from a Saddle Connection in Functional Differential Equations written by Hans-Otto Walther and published by . This book was released on 1990 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Shangjiang Guo
Publisher : Springer Science & Business Media
ISBN 13 : 1461469929
Total Pages : 295 pages
Book Rating : 4.4/5 (614 download)
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).
Author : Antonio F. Ize
Publisher :
ISBN 13 : 9783662214510
Total Pages : 436 pages
Book Rating : 4.2/5 (145 download)
Download or read book Functional Differential Equations and Bifurcation written by Antonio F. Ize and published by . This book was released on 2014-01-15 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Odo Diekmann
Publisher : Springer Science & Business Media
ISBN 13 : 1461242061
Total Pages : 547 pages
Book Rating : 4.4/5 (612 download)
Download or read book Delay Equations written by Odo Diekmann and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim here is to provide an introduction to the mathematical theory of infinite dimensional dynamical systems by focusing on a relatively simple - yet rich - class of examples, delay differential equations. This textbook contains detailed proofs and many exercises, intended both for self-study and for courses at graduate level, as well as a reference for basic results. As the subtitle indicates, this book is about concepts, ideas, results and methods from linear functional analysis, complex function theory, the qualitative theory of dynamical systems and nonlinear analysis. The book provides the reader with a working knowledge of applied functional analysis and dynamical systems.
Author : Hans-Otto Walther
Publisher : American Mathematical Soc.
ISBN 13 : 0821824678
Total Pages : 113 pages
Book Rating : 4.8/5 (218 download)
Download or read book Hyperbolic Periodic Solutions, Heteroclinic Connections and Transversal Homoclinic Points in Autonomous Differential Delay Equations written by Hans-Otto Walther and published by American Mathematical Soc.. This book was released on 1989 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : David John Warwick Simpson
Publisher : World Scientific
ISBN 13 : 9814293849
Total Pages : 255 pages
Book Rating : 4.8/5 (142 download)
Download or read book Bifurcations in Piecewise-smooth Continuous Systems written by David John Warwick Simpson and published by World Scientific. This book was released on 2010 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Real-world systems that involve some non-smooth change are often well-modeled by piecewise-smooth systems. However there still remain many gaps in the mathematical theory of such systems. This doctoral thesis presents new results regarding bifurcations of piecewise-smooth, continuous, autonomous systems of ordinary differential equations and maps. Various codimension-two, discontinuity induced bifurcations are unfolded in a rigorous manner. Several of these unfoldings are applied to a mathematical model of the growth of Saccharomyces cerevisiae (a common yeast). The nature of resonance near border-collision bifurcations is described; in particular, the curious geometry of resonance tongues in piecewise-smooth continuous maps is explained in detail. NeimarkSacker-like border-collision bifurcations are both numerically and theoretically investigated. A comprehensive background section is conveniently provided for those with little or no experience in piecewise-smooth systems.
Author : Christiane Rousseau
Publisher : Springer Science & Business Media
ISBN 13 : 9781402019296
Total Pages : 548 pages
Book Rating : 4.0/5 (192 download)
Download or read book Normal Forms, Bifurcations and Finiteness Problems in Differential Equations written by Christiane Rousseau and published by Springer Science & Business Media. This book was released on 2004-02-29 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the Nato Advanced Study Institute, held in Montreal, Canada, from 8 to 19 July 2002
Author : John H. Hubbard
Publisher : Springer Science & Business Media
ISBN 13 : 1461241928
Total Pages : 612 pages
Book Rating : 4.4/5 (612 download)
Download or read book Differential Equations: A Dynamical Systems Approach written by John H. Hubbard and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a continuation of the subject matter discussed in the first book, with an emphasis on systems of ordinary differential equations and will be most appropriate for upper level undergraduate and graduate students in the fields of mathematics, engineering, and applied mathematics, as well as in the life sciences, physics, and economics. After an introduction, there follow chapters on systems of differential equations, of linear differential equations, and of nonlinear differential equations. The book continues with structural stability, bifurcations, and an appendix on linear algebra. The whole is rounded off with an appendix containing important theorems from parts I and II, as well as answers to selected problems.
Author : S.-N. Chow
Publisher : Springer Science & Business Media
ISBN 13 : 1461381592
Total Pages : 529 pages
Book Rating : 4.4/5 (613 download)
Download or read book Methods of Bifurcation Theory written by S.-N. Chow and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: An alternative title for this book would perhaps be Nonlinear Analysis, Bifurcation Theory and Differential Equations. Our primary objective is to discuss those aspects of bifurcation theory which are particularly meaningful to differential equations. To accomplish this objective and to make the book accessible to a wider we have presented in detail much of the relevant background audience, material from nonlinear functional analysis and the qualitative theory of differential equations. Since there is no good reference for some of the mate rial, its inclusion seemed necessary. Two distinct aspects of bifurcation theory are discussed-static and dynamic. Static bifurcation theory is concerned with the changes that occur in the structure of the set of zeros of a function as parameters in the function are varied. If the function is a gradient, then variational techniques play an important role and can be employed effectively even for global problems. If the function is not a gradient or if more detailed information is desired, the general theory is usually local. At the same time, the theory is constructive and valid when several independent parameters appear in the function. In differential equations, the equilibrium solutions are the zeros of the vector field. Therefore, methods in static bifurcation theory are directly applicable.
Author : A. F. Ize
Publisher :
ISBN 13 :
Total Pages : 409 pages
Book Rating : 4.:/5 (8 download)
Download or read book Functional Differential Equations and Bifurcation written by A. F. Ize and published by . This book was released on 1980 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : John H. Hubbard
Publisher : Springer Science & Business Media
ISBN 13 : 9780387943770
Total Pages : 622 pages
Book Rating : 4.9/5 (437 download)
Download or read book Differential Equations: A Dynamical Systems Approach written by John H. Hubbard and published by Springer Science & Business Media. This book was released on 1991 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a continuation of the subject matter discussed in the first book, with an emphasis on systems of ordinary differential equations and will be most appropriate for upper level undergraduate and graduate students in the fields of mathematics, engineering, and applied mathematics, as well as in the life sciences, physics, and economics. After an introduction, there follow chapters on systems of differential equations, of linear differential equations, and of nonlinear differential equations. The book continues with structural stability, bifurcations, and an appendix on linear algebra. The whole is rounded off with an appendix containing important theorems from parts I and II, as well as answers to selected problems.
Author : Freddy Dumortier
Publisher : Springer
ISBN 13 : 3540384332
Total Pages : 234 pages
Book Rating : 4.5/5 (43 download)
Download or read book Bifurcations of Planar Vector Fields written by Freddy Dumortier and published by Springer. This book was released on 2006-12-08 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book reports on recent work by the authors on the bifurcation structure of singular points of planar vector fields whose linear parts are nilpotent. The bifurcation diagrams of the most important codimension-three cases are studied in detail. The results presented reach the limits of what is currently known on the bifurcation theory of planar vector fields. While the treatment is geometric, special analytical tools using abelian integrals are needed, and are explicitly developed. The rescaling and normalization methods are improved for application here. The reader is assumed to be familiar with the elements of Bifurcation and Dynamical Systems Theory. The book is addressed to researchers and graduate students working in Ordinary Differential Equations and Dynamical Systems, as well as anyone modelling complex multiparametric phenomena.
Author : Jack K. Hale
Publisher : American Mathematical Soc.
ISBN 13 : 9780821888926
Total Pages : 92 pages
Book Rating : 4.8/5 (889 download)
Download or read book Topics in Dynamic Bifurcation Theory written by Jack K. Hale and published by American Mathematical Soc.. This book was released on 1980 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Kevin E.M. Church
Publisher : Springer
ISBN 13 : 9783030645328
Total Pages : 388 pages
Book Rating : 4.6/5 (453 download)
Download or read book Bifurcation Theory of Impulsive Dynamical Systems written by Kevin E.M. Church and published by Springer. This book was released on 2021-03-25 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 : Bo Deng
Publisher :
ISBN 13 :
Total Pages : 188 pages
Book Rating : 4.3/5 (129 download)
Download or read book Bifurcation of a Unique Stable Periodic Orbit from a Homoclinic Orbit in Infinite Dimensional Systems written by Bo Deng and published by . This book was released on 1987 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jack K. Hale
Publisher : Springer
ISBN 13 : 0387971416
Total Pages : 574 pages
Book Rating : 4.3/5 (879 download)
Download or read book Dynamics and Bifurcations written by Jack K. Hale and published by Springer. This book was released on 1996-12-01 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, due primarily to the proliferation of computers, dynamical systems has again returned to its roots in applications. It is the aim of this book to provide undergraduate and beginning graduate students in mathematics or science and engineering with a modest foundation of knowledge. Equations in dimensions one and two constitute the majority of the text, and in particular it is demonstrated that the basic notion of stability and bifurcations of vector fields are easily explained for scalar autonomous equations. Further, the authors investigate the dynamics of planar autonomous equations where new dynamical behavior, such as periodic and homoclinic orbits appears.
Author : David H. Sattinger
Publisher : Springer
ISBN 13 : 3540383336
Total Pages : 197 pages
Book Rating : 4.5/5 (43 download)
Download or read book Topics in Stability and Bifurcation Theory written by David H. Sattinger and published by Springer. This book was released on 2006-11-15 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt:
