Hopf bifurcation of relative periodic solutions in a system of five passively mode-locked lasers

Abstract

The goal of this paper is to study the equivariant Hopf bifurcation of relative periodic solutions from relative equilibria in a system of five identical passively mode-locked semiconductor lasers coupled in the S 5-equivariant fashion. Each laser is described by a delay differential model respecting a spacial S 1-symmetry. The existence of branches of relative periodic solutions together with their symmetric classification is established using the equivariant twisted S 5 × S 1-degree with one free parameter. Theoretical results are supported by numerical simulations.