Involve: A Journal of Mathematics
- Volume 3, Number 3 (2010), 259-271.
Coexistence of stable ECM solutions in the Lang–Kobayashi system
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.
Involve, Volume 3, Number 3 (2010), 259-271.
Received: 15 September 2009
Revised: 6 August 2010
Accepted: 19 August 2010
First available in Project Euclid: 20 December 2017
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Mochan, Ericka; Buenger, Davis; Wiandt, Tamas. Coexistence of stable ECM solutions in the Lang–Kobayashi system. Involve 3 (2010), no. 3, 259--271. doi:10.2140/involve.2010.3.259. https://projecteuclid.org/euclid.involve/1513733317