  We investigate an integrable Hamiltonian modeling a heterotriatomic molecular
Bose-Einstein condensate. This model describes a mixture of two species of
atoms in different proportions, which can combine to form a triatomic molecule.
Beginning with a classical analysis, we determine the fixed points of the
system. Bifurcations of these points separate the parameter space into
different regions. Three distinct scenarios are found, varying with the atomic
population imbalance. This result suggests the ground-state properties of the
quantum model exhibit a sensitivity on the atomic population imbalance, which
is confirmed by a quantum analysis using different approaches, such as the
ground-state expectation values, the behavior of the quantum dynamics, the
energy gap, and the ground-state fidelity.
