Multiple scale analysis of delayed dynamical systems

G Giacomelli, A Politi

Research output: Contribution to journalArticlepeer-review

45 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)26-42
Number of pages17
JournalPhysica. D, Nonlinear Phenomena
Issue number1-4
Publication statusPublished - 15 Jun 1998


  • semiconductor-laser
  • feedback
  • chaos
  • instabilities


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