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Bifurcation From A Saddle Connection In Functional Differential Equations
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Book Synopsis Bifurcation from a Saddle Connection in Functional Differential Equations by : Hans-Otto Walther
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:
Book Synopsis Bifurcation Theory of Functional Differential Equations by : Shangjiang Guo
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).
Book Synopsis Functional Differential Equations and Bifurcation by : Antonio F. Ize
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:
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.
Book Synopsis Hyperbolic Periodic Solutions, Heteroclinic Connections and Transversal Homoclinic Points in Autonomous Differential Delay Equations by : Hans-Otto Walther
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:
Book Synopsis Bifurcations in Piecewise-smooth Continuous Systems by : David John Warwick Simpson
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)
Book Synopsis Normal Forms, Bifurcations and Finiteness Problems in Differential Equations by : Christiane Rousseau
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
Book Synopsis Differential Equations: A Dynamical Systems Approach by : John H. Hubbard
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.
Book Synopsis Methods of Bifurcation Theory by : S.-N. Chow
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.
Book Synopsis Functional Differential Equations and Bifurcation by : A. F. Ize
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:
Book Synopsis Differential Equations: A Dynamical Systems Approach by : John H. Hubbard
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.
Book Synopsis Bifurcations of Planar Vector Fields by : Freddy Dumortier
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.
Book Synopsis Topics in Dynamic Bifurcation Theory by : Jack K. Hale
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:
Book Synopsis Bifurcation Theory of Impulsive Dynamical Systems by : Kevin E.M. Church
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.
Book Synopsis Bifurcation of a Unique Stable Periodic Orbit from a Homoclinic Orbit in Infinite Dimensional Systems by : Bo Deng
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:
Book Synopsis Dynamics and Bifurcations by : Jack K. Hale
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.
Book Synopsis Topics in Stability and Bifurcation Theory by : David H. Sattinger
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: