Delay Differential Equations and Applications

List of figures. Preface. Contributing Authors. Introduction.- 1. History of Delay Equations J.K. Hale.- Part I General Results and Linear Theory of Delay Equations in Finite Dimensional Spaces. 2. Some General Results and Remarks on Delay Differential Equations E. Ait Dads. 3. Linear Autonomous Functional Differential Equations F. Kappel.- Part II Hopf Bifurcation, Centre Manifolds and Normal Forms for Delay Differential Equations. 4. Variation of Constant Formula for Delay Differential Equations M.L. Hbid, K. Ezzinbi. 5. Introduction to Hopf Bifurcation Theory for Delay Differential Equations M.L. Hbid. 6. An Algorithmic Scheme for Approximating Center Manifolds and Normal Forms for Functional Differential Equations M. Ait Babram. 7. Normal Forms and Bifurcations for Delay Differential Equations T. Faria.- Part III Functional Differential Equations in Infinite Dimensional Spaces. 8. A Theory of Linear Delay Differential Equations in Infinite Dimensional Spaces O. Arino, E. Sanchez. 9. The Basic Theory of Abstract Semilinear Functional Differential Equations with Non-Dense Domain K. Ezzinbi, M. Adimy.- Part IV More on Delay Differential Equations and Applications. 10. Dynamics of Delay Differential Equations H.O. Walther. 11. Delay Differential Equations in Single Species Dynamics Sh. Ruan. 12. Well-Posedness, Regularity and Asymptotic Behaviour of Retarded Differential Equations by Extrapolation Theory L. Maniar.- References.- Index.

[1]  Shui-Nee Chow,et al.  Existence of periodic solutions of autonomous functional differential equations , 1974 .

[2]  Richard Bellman,et al.  Differential-Difference Equations , 1967 .

[3]  Wolfgang Arendt,et al.  Resolvent Positive Operators , 1987 .

[4]  B. Hassard,et al.  Theory and applications of Hopf bifurcation , 1981 .

[5]  Jianhong Wu,et al.  Centre manifolds for partial differential equations with delays , 1992, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[6]  S. Bernfeld,et al.  Generalized hopf bifurcation and h-asymptotic stability , 1980 .

[7]  G. Sell,et al.  The Hopf Bifurcation and Its Applications , 1976 .

[8]  David Green,et al.  DIFFUSION AND HEREDITARY EFFECTS IN A CLASS OF POPULATION MODELS , 1981 .

[9]  F. Kappel.  LINEAR AUTONOMOUS FUNCTIONAL DIFFERENTIAL EQUATIONS , 2006 .

[10]  STABILITY IN A THREE-DIMENSIONAL SYSTEM OF DELAY-DIFFERENTIAL EQUATIONS , 2005 .

[11]  Jack K. Hale,et al.  On perturbations of delay-differential equations with periodic orbits , 2004 .

[12]  S. Lunel,et al.  Delay Equations. Functional-, Complex-, and Nonlinear Analysis , 1995 .

[13]  O. Arino,et al.  Linear theory of abstract functional differential equations of retarded type , 1995 .

[14]  Angus E. Taylor.  Introduction to functional analysis , 1959 .

[15]  Frank Neubrander,et al.  INTEGRATED SEMIGROUPS AND THEIR APPLICATIONS TO THE ABSTRACT CAUCHY PROBLEM , 1988 .

[16]  Jack K. Hale,et al.  Period Doubling in Singularly Perturbed Delay Equations , 1994 .

[17]  James A. Yorke,et al.  Ordinary differential equations which yield periodic solutions of differential delay equations , 1974 .

[18]  C. Travis,et al.  Existence and stability for partial functional differential equations , 1974 .

[19]  Shui-Nee Chow,et al.  Integral averaging and bifurcation , 1977 .

[20]  Matthias Hieber,et al.  Integrated Semigroups , 2003 .

[21]  Jianhong Wu,et al.  Smoothness of Center Manifolds for Maps and Formal Adjoints for Semilinear FDEs in General Banach Spaces , 2002, SIAM J. Math. Anal..

[22]  L. Magalhães,et al.  Normal Forms for Retarded Functional Differential Equations with Parameters and Applications to Hopf Bifurcation , 1995 .

[23]  A. Herz.  Solutions of ẋ(t)=−g(x(t−1)) Approach the Kaplan-Yorke Orbits for Odd Sigmoid g , 1995 .

[24]  Harlan W. Stech,et al.  The Hopf bifurcation: A stability result and application , 1979 .

[25]  W. Fitzgibbon,et al.  Semilinear functional differential equations in Banach space , 1978 .

[26]  P. Massatt.  Attractivity properties of α-contractions☆ , 1983 .

[27]  A. Liapounoff,et al.  Problème général de la stabilité du mouvement , 1907 .

[28]  Daniel B. Henry.  Topics in analysis , 1987 .

[29]  Fotios Giannakopoulos,et al.  Bifurcations in a planar system of differential delay equations modeling neural activity , 2001 .

[30]  Wolfgang Hahn,et al.  Stability of Motion , 1967 .

[31]  On asymptotic stability for linear delay equations , 1991 .

[32]  T. Faria.  On a Planar System Modelling a Neuron Network with Memory , 2000 .

[33]  Jack K. Hale,et al.  Sufficient conditions for stability and instability of autonomous functional- Differential equations. , 1965 .

[34]  W. H. Summers,et al.  Linearized Stability for Abstract Differential Equations with Delay , 1996 .

[35]  Daniel B. Henry.  Geometric Theory of Semilinear Parabolic Equations , 1989 .

[36]  André Vanderbauwhede,et al.  Center Manifold Theory in Infinite Dimensions , 1992 .

[37]  K. Kunisch,et al.  Necessary conditions for partial differential equations with delay to generate C0-semigroups , 1983 .

[38]  O. Arino,et al.  Approximation Scheme of a Center Manifold for Functional Differential Equations , 1997 .

[39]  Teresa Faria,et al.  Normal forms for semilinear functional differential equations in Banach spaces and applications. Part II , 2000 .

[40]  L. Salvadori,et al.  Attractivity and Hopf bifurcation , 1979 .

[41]  Jianhong Wu.  Theory and Applications of Partial Functional Differential Equations , 1996 .

[42]  K. P. Hadeler,et al.  Periodic solutions of difference-differential equations , 1977 .

[43]  B. Levinger,et al.  A folk theorem in functional differential equations , 1968 .

[44]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.

[45]  S. Bernfeld,et al.  Quasi-invariant manifolds, stability, and generalized Hopf bifurcation , 1982 .

[46]  Amnon Pazy,et al.  Semigroups of Linear Operators and Applications to Partial Differential Equations , 1992, Applied Mathematical Sciences.

[47]  Teresa Faria,et al.  Stability and Bifurcation for a Delayed Predator–Prey Model and the Effect of Diffusion☆ , 2001 .

[48]  Margaret C. Memory.  Stable and unstable manifolds for partial functional differential equations , 1991 .

[49]  Horst R Thiemea.  “Integrated semigroups” and integrated solutions to abstract Cauchy problems , 1990 .

[50]  J. Hale.  Theory of Functional Differential Equations , 1977 .

[51]  Roger D. Nussbaum,et al.  Periodic solutions of some nonlinear autonomous functional differential equations , 1974 .

[52]  Variation of constants formulas for partial differential equations with delay , 1981 .

[53]  Jack K. Hale,et al.  Large Diffusivity and Asymptotic Behavior in Parabolic Systems. , 1986 .

[54]  Richard Bellman,et al.  Asymptotic behavior of solutions of differential-difference equations , 1959 .

[55]  L. Magalhães,et al.  Normal Forms for Retarded Functional Differential Equations and Applications to Bogdanov-Takens Singularity , 1995 .

[56]  J. P. Lasalle,et al.  Theory of a general class of dissipative processes. , 1972 .

[57]  Periodic solutions for: ẋ(t) = λf(x(t),x(t – 1)) , 1988 .

[58]  O. Arino,et al.  A variation of constants formula for an abstract functional-differential equation of retarded type , 1996, Differential and Integral Equations.

[59]  R. Mañé,et al.  On the dimension of the compact invariant sets of certain non-linear maps , 1981 .

[60]  T. Faria.  Normal forms for periodic retarded functional differential equations , 1997, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[61]  Jianhong Wu,et al.  Synchronization and stable phase-locking in a network of neurons with memory , 1999 .

[62]  N. Chafee.  A bifurcation problem for a functional differential equation of finitely retarded type , 1971 .

[63]  Odo Diekmann,et al.  Perturbation theory for dual semigroups , 1987 .

[64]  Roger D. Nussbaum,et al.  The range of periods of periodic solutions of x′(t) = − αf(x(t − 1)) , 1977 .

[65]  W. Ruess.  Existence and stability of solutions to partial functional-differential equations with delay , 1999, Advances in Differential Equations.

[66]  O. Arino,et al.  Computational Scheme of a Center Manifold for Neutral Functional Differential Equations , 2001 .

[67]  M. Adimy.  Integrated Semigroups and Delay Differential Equations , 1993 .

[68]  Glenn F. Webb,et al.  Partial differential equations with deviating arguments in the time variable , 1976 .

[69]  Dongmei Xiao,et al.  Multiple Bifurcations in a Delayed Predator–prey System with Nonmonotonic Functional Response , 2022 .

[70]  J. Mallet-Paret.  Generic periodic solutions of functional differential equations , 1977 .

[71]  Hans-Otto Walther,et al.  A theorem on the amplitudes of periodic solutions of differential delay equations with applications to bifurcation , 1978 .

[72]  J. Cushing.  Periodic solutions of two species interaction models with lags , 1976 .

[73]  Teresa Faria,et al.  Normal forms and Hopf bifurcation for partial differential equations with delays , 2000 .

[74]  Jack K. Hale,et al.  Square and Pulse Waves with Two Delays , 2000 .

[75]  Floris Takens,et al.  Unfoldings of certain singularities of vectorfields: Generalized Hopf bifurcations , 1973 .

[76]  Kolmanovskii,et al.  Introduction to the Theory and Applications of Functional Differential Equations , 1999 .

[77]  Jack K. Hale,et al.  Fixed point theorems and dissipative processes. , 1973 .

[78]  R. Grimmer.  Existence of periodic solutions of functional differential equations , 1979 .

[79]  Y. Kitamura,et al.  ON A CLASS OF FUNCTIONAL DIFFERENTIAL EQUATIONS OF NEUTRAL TYPE , 1992 .

[80]  G. Prato,et al.  Differential operators with non dense domain , 1987 .

[81]  R. B. Grafton,et al.  A periodicity theorem for autonomous functional differential equations , 1969 .

[82]  Wenzhang Huang,et al.  Stability and Hopf Bifurcation for a Population Delay Model with Diffusion Effects , 1996 .

[83]  J. Hale,et al.  Exponential estimates and the saddle point property for neutral functional differential equations , 1971 .

[84]  J. Hale,et al.  Methods of Bifurcation Theory , 1996 .

[85]  G. Webb.  Theory of Nonlinear Age-Dependent Population Dynamics , 1985 .

[86]  Jack K. Hale,et al.  Critical cases for neutral functional differential equations , 1971 .