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Versal unfoldings for linear retarded functional differential equations

2003; Elsevier BV; Volume: 193; Issue: 2 Linguagem: Inglês

10.1016/s0022-0396(03)00092-5

1090-2732

Pietro-Luciano Buono, Victor G. LeBlanc,

Stability and Controllability of Differential Equations

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.