Bifurcation Theory of Functional Differential Equations

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

Download Bifurcation Theory of Functional Differential Equations Book in PDF, Epub and Kindle

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

Functional Differential Equations and Bifurcation
Title Functional Differential Equations and Bifurcation PDF eBook
Author Antonio F. Ize
Publisher Springer
Pages 435
Release 2006-11-14
Genre Science
ISBN 3540392513

Download Functional Differential Equations and Bifurcation Book in PDF, Epub and Kindle

Bifurcation Theory of Functional Differential Equations

Bifurcation Theory of Functional Differential Equations
Title Bifurcation Theory of Functional Differential Equations PDF eBook
Author Shangjiang Guo
Publisher Springer
Pages 289
Release 2013-07-30
Genre Mathematics
ISBN 9781461469919

Download Bifurcation Theory of Functional Differential Equations Book in PDF, Epub and Kindle

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).

Bifurcation Theory of Impulsive Dynamical Systems

Bifurcation Theory of Impulsive Dynamical Systems
Title Bifurcation Theory of Impulsive Dynamical Systems PDF eBook
Author Kevin E.M. Church
Publisher Springer Nature
Pages 388
Release 2021-03-24
Genre Mathematics
ISBN 3030645339

Download Bifurcation Theory of Impulsive Dynamical Systems Book in PDF, Epub and Kindle

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.

Functional Differential Equations and Bifurcation

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

Download Functional Differential Equations and Bifurcation Book in PDF, Epub and Kindle

Theory of Functional Differential Equations

Theory of Functional Differential Equations
Title Theory of Functional Differential Equations PDF eBook
Author Jack K. Hale
Publisher Springer Science & Business Media
Pages 374
Release 2012-12-06
Genre Mathematics
ISBN 146129892X

Download Theory of Functional Differential Equations Book in PDF, Epub and Kindle

Since the publication of my lecture notes, Functional Differential Equations in the Applied Mathematical Sciences series, many new developments have occurred. As a consequence, it was decided not to make a few corrections and additions for a second edition of those notes, but to present a more compre hensive theory. The present work attempts to consolidate those elements of the theory which have stabilized and also to include recent directions of research. The following chapters were not discussed in my original notes. Chapter 1 is an elementary presentation of linear differential difference equations with constant coefficients of retarded and neutral type. Chapter 4 develops the recent theory of dissipative systems. Chapter 9 is a new chapter on perturbed systems. Chapter 11 is a new presentation incorporating recent results on the existence of periodic solutions of autonomous equations. Chapter 12 is devoted entirely to neutral equations. Chapter 13 gives an introduction to the global and generic theory. There is also an appendix on the location of the zeros of characteristic polynomials. The remainder of the material has been completely revised and updated with the most significant changes occurring in Chapter 3 on the properties of solutions, Chapter 5 on stability, and Chapter lOon behavior near a periodic orbit.

Topics in Dynamic Bifurcation Theory

Topics in Dynamic Bifurcation Theory
Title Topics in Dynamic Bifurcation Theory PDF eBook
Author Jack K. Hale
Publisher American Mathematical Soc.
Pages 90
Release 1981-12-31
Genre Mathematics
ISBN 0821816985

Download Topics in Dynamic Bifurcation Theory Book in PDF, Epub and Kindle

Presents the general theory of first order bifurcation that occur for vector fields in finite dimensional space. This book includes formulation of structural stability and bifurcation in infinite dimensions.