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When studying a general system of delay differential equation with a singleconstant delay, we encounter a certain lack of uniqueness in determining thecoefficient of one of the third order terms of the series defining the centermanifold. We solve this problem by considering a perturbation of the consideredproblem, perturbation that allows us to remove the singularity. The resultgeneralizes a similar result obtained for scalar differential equations (J.Dyn. Diff. Eqns., 24/2012).

On the computation of the third order terms of the series defining the center manifold for systems of delay differential equation