  We study a two-state quantum system with a non linearity intended to describe
interactions with a complex environment, arising through a non local coupling
term. We study the stability of particular solutions, obtained as constrained
extrema of the energy functional of the system. The simplicity of the model
allows us to justify a complete stability analysis. This is the opportunity to
review in details the techniques to investigate the stability issue. We also
bring out the limitations of perturbative approaches based on simpler
asymptotic models.
