A perturbed Hopf bifurcation with reflection symmetry

Abstract

SynopsisWe study the effects of a small symmetry breaking perturbation on a system of differential equations at a coupled Hopf bifurcation with O(2) symmetry, where the perturbation breaks the continuous rotation symmetry, but retains a reflection (Z2) symmetry. It is shown that for a large range of parameter values, the invariant manifolds of the unperturbed bifurcation persist and that for some values of normal form coefficients there are secondary bifurcations of nonsymmetric periodic standing wave solutions.