Bifurcation from a Saddle Connection in Functional Differential Equations
Title | Bifurcation from a Saddle Connection in Functional Differential Equations PDF eBook |
Author | Hans-Otto Walther |
Publisher | |
Pages | 84 |
Release | 1990 |
Genre | Bifurcation theory |
ISBN |
Bifurcation Theory of Functional Differential Equations
Title | Bifurcation Theory of Functional Differential Equations PDF eBook |
Author | Shangjiang Guo |
Publisher | Springer Science & Business Media |
Pages | 295 |
Release | 2013-07-30 |
Genre | Mathematics |
ISBN | 1461469929 |
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).
Functional Differential Equations and Bifurcation
Title | Functional Differential Equations and Bifurcation PDF eBook |
Author | Antonio F. Ize |
Publisher | |
Pages | 436 |
Release | 2014-01-15 |
Genre | |
ISBN | 9783662214510 |
Delay Equations
Title | Delay Equations PDF eBook |
Author | Odo Diekmann |
Publisher | Springer Science & Business Media |
Pages | 547 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 1461242061 |
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.
Hyperbolic Periodic Solutions, Heteroclinic Connections and Transversal Homoclinic Points in Autonomous Differential Delay Equations
Title | Hyperbolic Periodic Solutions, Heteroclinic Connections and Transversal Homoclinic Points in Autonomous Differential Delay Equations PDF eBook |
Author | Hans-Otto Walther |
Publisher | American Mathematical Soc. |
Pages | 113 |
Release | 1989 |
Genre | Chaotic behavior in systems |
ISBN | 0821824678 |
Bifurcations in Piecewise-smooth Continuous Systems
Title | Bifurcations in Piecewise-smooth Continuous Systems PDF eBook |
Author | David John Warwick Simpson |
Publisher | World Scientific |
Pages | 255 |
Release | 2010 |
Genre | Science |
ISBN | 9814293849 |
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.
Normal Forms, Bifurcations and Finiteness Problems in Differential Equations
Title | Normal Forms, Bifurcations and Finiteness Problems in Differential Equations PDF eBook |
Author | Christiane Rousseau |
Publisher | Springer Science & Business Media |
Pages | 548 |
Release | 2004-02-29 |
Genre | Mathematics |
ISBN | 9781402019296 |
Proceedings of the Nato Advanced Study Institute, held in Montreal, Canada, from 8 to 19 July 2002