Normal Forms for Retarded Functional Differential Equations with Parameters and Applications to Hopf Bifurcation

✍ Scribed by T. Faria; L.T. Magalhaes

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 650 KB
• Volume: 122
• Category: Article
• ISSN: 0022-0396
• DOI: 10.1006/jdeq.1995.1144

✦ Synopsis

The paper addresses, for retarded functional differential equations (FDEs) with parameters, the computation of normal forms associated with the flow on a finitedimensional 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. ' 1995 Academic Press. Inc.