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2010 Coexistence of stable ECM solutions in the Lang–Kobayashi system
Ericka Mochan, Davis Buenger, Tamas Wiandt
Involve 3(3): 259-271 (2010). DOI: 10.2140/involve.2010.3.259

Abstract

The Lang–Kobayashi system of delay differential equations describes the behavior of the complex electric field and inversion N 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.

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Ericka Mochan. Davis Buenger. Tamas Wiandt. "Coexistence of stable ECM solutions in the Lang–Kobayashi system." Involve 3 (3) 259 - 271, 2010. https://doi.org/10.2140/involve.2010.3.259

Information

Received: 15 September 2009; Revised: 6 August 2010; Accepted: 19 August 2010; Published: 2010
First available in Project Euclid: 20 December 2017

zbMATH: 1211.34105
MathSciNet: MR2739518
Digital Object Identifier: 10.2140/involve.2010.3.259

Subjects:
Primary: 37G35, 37M20, 78A60

Rights: Copyright © 2010 Mathematical Sciences Publishers

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