Translator Disclaimer
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


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.


Download Citation

Ericka Mochan. Davis Buenger. Tamas Wiandt. "Coexistence of stable ECM solutions in the Lang–Kobayashi system." Involve 3 (3) 259 - 271, 2010.


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

Primary: 37G35, 37M20, 78A60

Rights: Copyright © 2010 Mathematical Sciences Publishers


Vol.3 • No. 3 • 2010
Back to Top