  Dynamical instability is an inherent feature of bosonic systems described by
the Bogoliubov de Geenes (BdG) Hamiltonian. Since it causes the BdG system to
collapse, it is generally thought that it should be avoided. Recently, there
has been much effort to harness this instability for the benefit of creating a
topological amplifier with stable bulk bands but unstable edge modes which can
be populated at an exponentially fast rate. We present a theorem for
determining the stability of states with energies sufficiently away from zero,
in terms of an unconventional commutator between the number conserving part and
number nonconserving part of the BdG Hamiltonian. We apply the theorem to a
generalization of a model from Galilo et al. [Phys. Rev. Lett, 115,
245302(2015)] for creating a topological amplifier in an interacting spin-1
atom system in a honeycomb lattice through a quench process. We use this model
to illustrate how the vanishing of the unconventional commutator selects the
symmetries for a system so that its bulk states are stable against (weak)
pairing interactions. We find that as long as time reversal symmetry is
preserved, our system can act like a topological amplifier, even in the
presence of an onsite staggered potential which breaks the inversion symmetry.
