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Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation. (English) Zbl 0836.34068
From authors’ abstract: “The paper addresses, for retarded functional differential equations (FDEs) with parameters, the computation of normal forms associated with the flow on a finite-dimensional invariant manifold tangent to an invariant space for the infinitesimal generator of the linearized equation at a singularity. The analysis is based on the theory previously developed for FDEs without parameters by considering an extension of a phase space appropriate to the computation of these normal forms. As an application, the generic Hopf bifurcation for scalar retarded FDEs is considered”.

34K05General theory of functional-differential equations
34C20Transformation and reduction of ODE and systems, normal forms
34C23Bifurcation (ODE)