Dynamics of Lang-Kobayashi Equations with Large Control Coe cient

Abstract

We study the system of delayed di˙erential equations modeling the dynamics of semiconductor laser with optical feedback (Lang-Kobayashi model). In the case of instability of external cavity modes we derive the ensembles of quasi-normal forms which appear to be the parabolic (or degenerate parabolic) partial di˙erential equations for slowly varied amplitude of the electric field. Coexistence of a large number of multi-frequency oscillatory regimes is discussed.