## Zalman Balanov, Pavel Kravetc, Wieslaw Krawcewicz, Dmitrii Rachinskii, Hao-pin Wu, Hopf bifurcation of relative periodic solutions in a system of five passively mode-locked lasers

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DOI: 10.23952/jnva.2.2018.2.10
Volume 2, Issue 2, 1 August 2018, Pages 233-262

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 $S_5 \times S^1$-degree with one free parameter. Theoretical results are supported by numerical simulations.