Center manifolds and normal forms for a class of retarded functional differential equations with parameter associated with Fold-Hopf singularity

In this paper, we present explicit formulas for computing the coefficients of a center manifolds for the Fold-Hopf singularity in autonomous retarded functional differential equations. As consequence, normal forms associated with the flow on a center manifold up to an arbitrary order are derived. The explicit formulas have been implemented using the computer algebra system Maple. We apply our results to a delayed system in order to show the applicability of the methodology.