Versal unfoldings for linear retarded functional differential equations
Dynamical Systems
2007-05-23 v1
Abstract
We consider parametrized families of linear retarded functional differential equations (RFDEs) projected onto finite-dimensional invariant manifolds, and address the question of versality of the resulting parametrized family of linear ordinary differential equations. A sufficient criterion for versality is given in terms of readily computable quantities. In the case where the unfolding is not versal, we show how to construct a perturbation of the original linear RFDE (in terms of delay differential operators) whose finite-dimensional projection generates a versal unfolding. We illustrate the theory with several examples, and comment on the applicability of these results to bifurcation analyses of nonlinear RFDEs.
Cite
@article{arxiv.math/0208143,
title = {Versal unfoldings for linear retarded functional differential equations},
author = {Pietro-Luciano Buono and Victor G. LeBlanc},
journal= {arXiv preprint arXiv:math/0208143},
year = {2007}
}