Normal forms and Hopf bifurcation for partial differential equations with delays

Abstract

The paper addresses the computation of normal forms for some Partial Functional Differential Equations (PFDEs) near equilibria. The analysis is based on the theory previously developed for autonomous retarded Functional Differential Equations and on the existence of center (or other invariant) manifolds. As an illustration of this procedure, two examples of PFDEs where a Hopf singularity occurs on the center manifold are considered.