  We study exactly soluble system of trapped bosonic particles interacting by a
model harmonic forces. The model allows for detailed examination of the order
parameter (condensate wave function) as well as concept of the off-diagonal and
diagonal order. We analyze the effect of interactions on the condensate and
show that sufficiently strong interactions, attractive or repulsive, lead to
destruction of the condensate. In the thermodynamic limit this destruction has
a critical character. It is shown that the existence of the coherent state of
bosons is related to existence of two length scales determined by one- and
two-particle reduced density matrices. The condensate can exist only if the two
length scales are of the same order. Interactions, both repulsive and
attractive, change their relative size which may lead to destruction of
coherence in the system and depletion of the condensate. We suggest that this
scenario is model independent.
