1. Classification of Codimension-One Bifurcations in a Tetrad of Lasers with Feed Forward Coupling.
- Author
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Domogo, Andrei A. and Collera, Juancho A.
- Subjects
- *
SEMICONDUCTOR lasers , *BIFURCATION theory , *SYMMETRY groups , *DELAY differential equations , *ISOTROPY subgroups - Abstract
We consider a model of a tetrad of semiconductor lasers with unidirectional coupling. This system is described by Lang-Kobayashi (LK) rate equations, which is a system of delay differential equations with one fixed delay. Basic solutions to this system are called compound laser modes (CLMs). We classify the CLMs of this four-laser system according to their symmetry. The symmetric CLMs are identified by looking at the isotropy subgroups of the symmetry group of this system. Numerical continuation in DDE-Biftool generates a branch of symmetric CLMs. We then find steady-state and Hopf bifurcations along the branch of fully symmetric CLMs and identify those that are symmetrybreaking and symmetry-preserving. Finally, we use the Equivariant Branching Lemma and Equivariant Hopf Theorem to establish the existence of emanating branches of solutions from symmetry-breaking bifurcations. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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