Affordable Access

Publisher Website

Versal unfoldings for linear retarded functional differential equations

Authors
Journal
Journal of Differential Equations
0022-0396
Publisher
Elsevier
Publication Date
Volume
193
Issue
2
Identifiers
DOI: 10.1016/s0022-0396(03)00092-5
Disciplines
  • Mathematics

Abstract

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.

There are no comments yet on this publication. Be the first to share your thoughts.