LEADER 04467oam 2200577 450 001 9910741179603321 005 20190911103512.0 010 $a1-4614-6992-9 024 7 $a10.1007/978-1-4614-6992-6 035 $a(OCoLC)856996154 035 $a(MiFhGG)GVRL6YWI 035 $a(EXLCZ)992670000000530463 100 $a20130318d2013 uy 0 101 0 $aeng 135 $aurun|---uuuua 181 $ctxt 182 $cc 183 $acr 200 10$aBifurcation theory of functional differential equations /$fShangjiang Guo, Jianhong Wu 205 $a1st ed. 2013. 210 1$aNew York :$cSpringer,$d2013. 215 $a1 online resource (ix, 289 pages) $cillustrations 225 1 $aApplied Mathematical Sciences,$x0066-5452 ;$v184 300 $a"ISSN: 0066-5452." 311 $a1-4614-6991-0 311 $a1-4899-8896-3 320 $aIncludes bibliographic references and index. 327 $a""1.9.3 Folda???Hopf Bifurcation""""1.9.4 Bautin Bifurcation""; ""1.9.5 Hopfa???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"" 327 $a""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 Lyapunova???Schmidt Reduction""; ""5.1 The Lyapunova???Schmidt Method""; ""5.2 Derivatives of the Bifurcation Equation""; ""5.3 Equivariant Equations"" 327 $a""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 Leraya???Schauder Degree""; ""6.4 Global Bifurcation Theorem""; ""6.5 S1-Equivariant Degree""; ""6.5.1 Differentiability Case""; ""6.5.2 Nondifferentiability Case"" 327 $a""6.6 Global Hopf Bifurcation Theory of DDEs"" 330 $aThis book  provides a crash course on  various methods from the bifurcation theory of Functional Differential Equations (FDEs). FDEs arise very naturally in economics, life sciences and engineering  and the study of FDEs has been a major source of inspiration for advancement in nonlinear analysis and infinite dimensional dynamical systems. The  book summarizes some practical and general approaches and frameworks for the investigation of bifurcation phenomena of FDEs depending on parameters. The book aims to be self-contained so the readers will find in this book all relevant materials in bifurcation, dynamical systems with symmetry, functional differential equations, normal forms and center manifold reduction. This material was used in graduate courses on functional differential equations at Hunan University (China) and York University (Canada). 410 0$aApplied mathematical sciences (Springer-Verlag New York Inc.) ;$vv. 184. 606 $aBifurcation theory 606 $aFunctional differential equations 606 $aBifurcation theory$2fast 606 $aFunctional differential equations$2fast 615 0$aBifurcation theory. 615 0$aFunctional differential equations. 615 7$aBifurcation theory. 615 7$aFunctional differential equations. 676 $a515.355 676 $a515.392 700 $aGuo$b Shangjiang$4aut$4http://id.loc.gov/vocabulary/relators/aut$01424698 702 $aWu$b Jianhong$f1964- 801 0$bMiFhGG 801 1$bMiFhGG 906 $aBOOK 912 $a9910741179603321 996 $aBifurcation Theory of Functional Differential Equations$93554166 997 $aUNINA