In this memoire we try to contribute to the study of the instabilities that arise when a semiconductor laser is subject to a given type of perturbation. In special, in the forthcoming chapters the dynamical consequences of bidirectionally couple two semiconductor lasers are studied. In this configuration of mutually coupled lasers, the behavior of each laser depends on the state of the other through a given interaction. In our case the coupling is optoelectronic, i.e., part of the light emitted by each laser is detected and the photocurrent generated is added to the bias current of the other laser. Both the absolute and relative dynamics between the lasers, and the synchronization phenomenon will be evaluated in this system. In spite of the fact that the results here presented have been exclusively predicted for the coupling of semiconductor lasers, most of the phenomena we investigate seem to be independent of the particular characteristics of this type of laser and therefore they are expected to occur in more general models of coupled oscillators with time delay. In fact, not only semiconductor lasers but neurons, chemical oscillators, or Josephson junctions are just a few examples of non-linear systems, whose connection or coupling with similar units may lead to a very rich dynamics.
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