Hopf Bifurcations of Functional Differential Equations with Dihedral Symmetries

Abstract

We discuss the joint impact of temporal delay and spatial dihedral symmetries on the occurence and multiplicity of Hopf bifurcations for a system of FDEs. By applying the equivariant degree theory we establish a result on the existence of multiple branches of nonconstant periodic solutions and classify their symmetries. General results are illustrated by a ring of identical oscillators with identical coupling between adjacent cells. © 1998 Academic Press.