Versal unfoldings for linear retarded functional differential equations |
| |
Authors: | Pietro-Luciano Buono |
| |
Institution: | a Centre de Recherches Mathématiques, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal, Que, Canada H3C 3J7 b Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ont., Canada K1N 6N5 |
| |
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. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|