#### Vol. 3, No. 3, 2010

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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
##### Abstract

The Lang–Kobayashi system of delay differential equations describes the behavior of the complex electric field $\mathsc{ℰ}$ 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.

##### Keywords
delay differential equations, bifurcations, Lang–Kobayashi equations
##### Mathematical Subject Classification 2000
Primary: 37G35, 37M20, 78A60