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

  • Juancho A. ColleraEmail author
Conference paper


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 ×S1. 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.


SB Bifurcations Finite Propagation Time Numerical Bifurcation Analysis Hopf Bifurcation Delay Differential Equations 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work was funded by the UP System Emerging Interdisciplinary Research Program (OVPAA-EIDR-C03-011). The author also acknowledged the support of the UP Baguio through RLCs during the A.Y. 2014–2015.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of the Philippines BaguioBaguio CityPhilippines

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