Equivariant Hopf bifurcation for neutral functional differential equations

Abstract

In this paper we employ an equivariant Lyapunov-Schmidt procedure to give a clearer understanding of the one-to-one correspondence of the periodic solutions of a system of neutral functional differential equations with the zeros of the reduced bifurcation map, and then set up equivariant Hopf bifurcation theory. In the process we derive criteria for the existence and direction of branches of bifurcating periodic solutions in terms of the original system, avoiding the process of center manifold reduction.