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Coexistence of
stable ECM solutions in the Lang–Kobayashi system
Ericka Mochan, C. Davis Buenger and Tamas Wiandt
Vol. 3 (2010), No. 3, 259–271
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Abstract |
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The Lang–Kobayashi system of delay differential equations describes the behavior of the complex electric field and inversion inside an external cavity semiconductor laser. This system has a family of special periodic solutions known as external cavity modes (ECMs). It is well known that these ECM solutions appear through saddle-node bifurcations, then lose stability through a Hopf bifurcation before new ECM solutions are born through a secondary saddle-node bifurcation. Employing analytical and numerical techniques, we show that for certain short external cavity lasers the loss of stability happens only after the secondary saddle-node bifurcations, which means that stable ECM solutions can coexist in these systems. We also investigate the basins of these ECM attractors. |
Keywords
delay differential equations, bifurcations, Lang–Kobayashi
equations
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Mathematical Subject Classification 2000
Primary: 37G35, 37M20, 78A60
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Milestones
Received: 15 September 2009
Revised: 6 August 2010
Accepted: 19 August 2010
Published: 16 October 2010
Communicated by John Baxley
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Authors |
| Ericka Mochan | |
| Department of Biomedical
Engineering Western New England College Springfield, MA 01119 United States |
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| C. Davis Buenger | |
| Department of Mathematics The Ohio State University Columbus, OH 43201 United States |
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| Tamas Wiandt | |
| School of Mathematical
Sciences Rochester Institute of Technology Rochester, NY 14623 United States |
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