Symmetry-Breaking Bifurcations in Laser Systems with All-to-All Coupling

Juancho A. Collera ()
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Juancho A. Collera: University of the Philippines Baguio, Department of Mathematics and Computer Science

A chapter in Mathematical and Computational Approaches in Advancing Modern Science and Engineering, 2016, pp 81-88 from Springer

Abstract: Abstract We consider a system of n semiconductor lasers with all-to-all coupling that is described using the Lang-Kobayashi rate equations. The lasers are coupled through their optical fields with delay arising from the finite propagation time of the light from one laser to another. As a consequence of the coupling structure, the resulting system of delay differential equations is equivariant under the symmetry group S n ×S 1. Since symmetry gives rise to eigenvalues of higher multiplicity, implementing a numerical bifurcation analysis to our laser system is not straightforward. Our results include the use of the equivariance property of the laser system to find symmetric solutions, and to correctly locate steady-state and Hopf bifurcations. Additionally, this method identifies symmetry-breaking bifurcations where new branches of solutions emerge.

Keywords: SB Bifurcations; Finite Propagation Time; Numerical Bifurcation Analysis; Hopf Bifurcation; Delay Differential Equations (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-30379-6_8

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DOI: 10.1007/978-3-319-30379-6_8

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