  We study the evolution of a system of interacting ultracold bosons, which
presents nonlinear, chaotic, behaviors in the limit of very large number of
particles. Using the spectral entropy as an indicator of chaos and three
different numerical approaches : Exact diagonalization, truncated Husimi method
and mean-field (Gross-Pitaevskii) approximation, we put into evidence the
destructive impact of quantum noise on the emergence of the nonlinear dynamics.
