  We report here an extensive study of sustained oscillations of the viscosity
of a complex fluid near an out-of-equilibrium transition. Using well defined
protocols, we perform rheological measurements of the onion texture near a
layering transition in a Couette flow. This complex fluid exhibits sustained
oscillations of the viscosity, on a large time scale (500s) at controlled
stress. These oscillations are directly correlated to an oscillating
microstrutural change of the texture of the fluid. We observe a great diversity
of dynamical behavior and we show that there is a coupling with spatial effects
in the gradient v direction. This is in agreement with a carefull analysis of
the temporal series of the viscosity with the dynamical system theory. This
analysis indicates that the observed dynamical responses do not strictly
correspond to 3-dimensional chaotic states, probably because some
spatio-temporal effects are present and are likely to play an important role.
