• Media type: Text; Report; E-Book
  • Title: Properties of stationary states of delay equations with large delay and applications to laser dynamics
  • Contributor: Yanchuk, Serhiy [Author]
  • Published: Weierstrass Institute for Applied Analysis and Stochastics publication server, 2004
  • Language: English
  • DOI: https://doi.org/10.20347/WIAS.PREPRINT.944
  • Keywords: delay equations -- large delay -- map -- Lang-Kobayashi system -- laser ; 34K06 ; 34K60 ; 34K20 ; article
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  • Description: 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 $\tau\to\infty$.