Multiple scale analysis of delayed dynamical systems

The model equations of a semiconductor laser with delayed feeback are studied as a prototype of general delayed systems in the case of long delay (thermodynamic limit). It is shown that its behaviour in the vicinity of the Hopf bifurcation can be described by suitable amplitude equations. The derivation of the final model follows naturally from the space-time representation of the evolution and by the corresponding re-formulation of the linear stability problem. Regions characterized by both direct and inverse Hopf bifurcations are found, and in particular, parameter values are identified for which a chaotic evolution is expected. Copyright (C) Elsevier Science B.V.