Generalized Hopf Bifurcation for Neutral Functional Differential Equations

Abstract

Here we employ the Lyapunov–Schmidt procedure to investigate bifurcations in a general neutral functional differential equation (NFDE) when the infinitesimal generator has, for a critical value of the parameter, a pair of nonsemisimple purely imaginary eigenvalues with multiplicity [Formula: see text]. We derive criteria, explicitly in terms of the system's parameter values, for the existence of two branches of bifurcating periodic solutions and for the description of the bifurcation direction of these branches. The general result is illustrated by a detailed case study of an oscillator.