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Ukrainian Mathematical Journal

, Volume 60, Issue 3, pp 495–507 | Cite as

Amplitude synchronization in a system of two coupled semiconductor lasers

  • S. V. Yanchuk
  • K. R. Schneider
  • O. B. Lykova
Article
  • 45 Downloads

Abstract

We consider a system of ordinary differential equations used to describe the dynamics of two coupled single-mode semiconductor lasers. In particular, we study solutions corresponding to the amplitude synchronization. It is shown that the set of these solutions forms a three-dimensional invariant manifold in the phase space. We study the stability of trajectories on this manifold both in the tangential direction and in the transverse direction. We establish conditions for the existence of globally asymptotically stable solutions of equations on the manifold synchronized with respect to the amplitude.

Keywords

Periodic Solution Equilibrium Position Semiconductor Laser Invariant Manifold Stable Periodic Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  • S. V. Yanchuk
    • 1
    • 2
    • 3
  • K. R. Schneider
    • 2
  • O. B. Lykova
    • 1
  1. 1.Institute of MathematicsUkrainian National Academy of SciencesKievUkraine
  2. 2.Weierstrass Institute for Applied Analysis and StochasticsBerlinGermany
  3. 3.Institute of MathematicsHumboldt UniversityBerlinGermany

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