Bifurcation Theory of Functional Differential Equations [electronic resource] /
Guo, Shangjiang.author.
Wu, Jianhong.author.
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. The 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).
Description based upon print version of record.
""1.9.3 Foldâ€?Hopf Bifurcation""""1.9.4 Bautin Bifurcation""; ""1.9.5 Hopfâ€?Hopf Bifurcation""; ""1.10 Some Other Bifurcations""; ""2 Introduction to Functional Differential Equations""; ""2.1 Infinite Dynamical Systems Generated by Time Lags""; ""2.2 The Framework for DDEs""; ""2.2.1 Definitions""; ""2.2.2 An Operator Equation""; ""2.2.3 Spectrum of the Generator""; ""2.2.4 An Adjoint Operator""; ""2.2.5 A Bilinear Form""; ""2.2.6 Neural Networks with Delay: A Case Studyon Characteristic Equations""; ""2.2.6.1 General Additive Neural Networks with Delay""
""4.2.2 Computation of Normal Forms""""4.2.2.1 The Matrix Method""; ""4.2.2.2 The Adjoint Operator Method""; ""4.2.3 Internal Symmetry""; ""4.3 Perturbed Vector Fields""; ""4.3.1 Normal Form for Hopf Bifurcation""; ""4.3.2 Norm Form Theorem""; ""4.3.3 Preservation of External Symmetry""; ""4.4 RFDEs with Symmetry""; ""4.4.1 Basic Assumptions""; ""4.4.2 Computation of Symmetric Normal Forms""; ""4.4.3 Nonresonance Conditions""; ""5 Lyapunovâ€?Schmidt Reduction""; ""5.1 The Lyapunovâ€?Schmidt Method""; ""5.2 Derivatives of the Bifurcation Equation""; ""5.3 Equivariant Equations""
""5.4 The Steady-State Equivariant Branching Lemma""""5.5 Generalized Hopf Bifurcation of RFDE""; ""5.6 Equivariant Hopf Bifurcation of NFDEs""; ""5.7 Application to a Delayed van der Pol Oscillator""; ""5.8 Applications to a Ring Network""; ""5.9 Coupled Systems of NFDEs and Lossless Transmission Lines""; ""5.10 Wave Trains in the FPU Lattice""; ""6 Degree Theory""; ""6.1 Introduction""; ""6.2 The Brouwer Degree""; ""6.3 The Lerayâ€?Schauder Degree""; ""6.4 Global Bifurcation Theorem""; ""6.5 S1-Equivariant Degree""; ""6.5.1 Differentiability Case""; ""6.5.2 Nondifferentiability Case""
""6.6 Global Hopf Bifurcation Theory of DDEs""
Includes bibliographic references and index.
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. The 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).
Difference equations.
Functional equations.
Dynamics.
Ergodic theory.
Differential equations.
Difference and Functional Equations.
Dynamical Systems and Ergodic Theory.
Ordinary Differential Equations.