WIAS Preprint No. 944, (2004)

Properties of stationary states of delay equations with large delay and applications to laser dynamics



Authors

  • Yanchuk, Serhiy

2010 Mathematics Subject Classification

  • 34K20 34K60 34K06

Keywords

  • delay equations, large delay, map, Lang-Kobayashi system, laser

Abstract

We consider properties of periodic solutions of the differential-delay system, which models a laser with optical feedback. In particular, we describe a set of multipliers for these solutions in the limit of large delay. As a preliminary result, we obtain conditions for stability of an equilibrium of a generic differential-delay system with fixed large delay $tau$. We also show a connection between characteristic roots of the equilibrium and multipliers of the mapping obtained via the formal limit $tautoinfty$.

Appeared in

  • Math. Meth. Appl. Sci. (2005) 28:363-377.

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