𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Computational Scheme of a Center Manifold for Neutral Functional Differential Equations

✍ Scribed by M. Ait Babram; O. Arino; M.L. Hbid

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
134 KB
Volume
258
Category
Article
ISSN
0022-247X

No coin nor oath required. For personal study only.

✦ Synopsis

This work addresses a computational algorithm of terms of a center manifold for neutral functional differential equations. The Bogdanov᎐Takens and the Hopf singularities are considered. Finally, as an illustration of our scheme, we give an example where the second term of a center manifold is explicitly determined.

πŸ“œ SIMILAR VOLUMES

Approximation Scheme of a Center Manifol
Approximation Scheme of a Center Manifold for Functional Differential Equations
✍ M.Ait Babram; M.L. Hbid; O. Arino πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 255 KB

In this paper, we consider a general autonomous functional differential equation having a local center manifold. Then, we give an algorithmic procedure to compute the terms in the Taylor expansion of this manifold up to any order.

Homoclinic Orbits on Invariant Manifolds
Homoclinic Orbits on Invariant Manifolds of a Functional Differential Equation
✍ Weinian Zhang; Jiongyu Wu πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 146 KB

Following the existence of generalized exponential dichotomies and corresponding invariant manifolds for functional differential equations, the homoclinic solution of a delay equation studied by Lin (1986, J. Differential Equations 63, 227 254) proved to be reducible to a finite dimensional one.

A Class of Linear Partial Neutral Functi
A Class of Linear Partial Neutral Functional Differential Equations with Nondense Domain
✍ Mostafa Adimy; Khalil Ezzinbi πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 498 KB

We consider a system of linear partial neutral functional differential equations with nondense domain. A natural generalized notion of solutions is provided by the integral solutions. We derive a variation-of-constants formula which allows us to transform the integral solutions of the neutral equati

Invariant Manifolds for a Class of Dispe
Invariant Manifolds for a Class of Dispersive, Hamiltonian, Partial Differential Equations
✍ Claude-Alain Pillet; C.Eugene Wayne πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 255 KB

We construct an invariant manifold of periodic orbits for a class of non-linear Schro dinger equations. Using standard ideas of the theory of center manifolds, we rederive the results of Soffer and Weinstein (Comm. Math. Phys. 133, 119 146 (1997); J. Differential Equations 98, 376 390 (1992)) on the