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

✍ Scribed by Serhiy Yanchuk

• Publisher: John Wiley and Sons
• Year: 2005
• Tongue: English
• Weight: 216 KB
• Volume: 28
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.584

✦ Synopsis

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 τ. We also show a connection between characteristic roots of the equilibrium and multipliers of the mapping obtained via the formal limit τ→∞. Copyright © 2004 John Wiley & Sons, Ltd.