  We examine the emergence of chaos in a non-linear model derived from a
semiquantum Hamiltonian describing the coupling between a classical field and a
quantum system. The latter corresponds to a bosonic version of a BCS-like
Hamiltonian, and possesses stable and unstable regimes. The dynamics of the
whole system is shown to be strongly influenced by the quantum subsystem. In
particular, chaos is seen to arise in the vicinity of a quantum critical case,
which separates the stable and unstable regimes of the bosonic system.
