  The role of repulsive interactions in statistical systems of Bose particles
is investigated. Three different phenomenological frameworks are considered: a
mean field model, an excluded volume model, and a model with a medium dependent
effective mass. All three models are tuned to yield similar equations of state,
with only minor deviations from the ideal Bose gas at small chemical
potentials. Our analysis indicates, however, that these models lead to
qualitatively different results for the Bose-Einstein condensation phenomenon.
We discuss the different aspects of this phenomenon, namely, an onset of the
Bose-Einstein condensation, particle number fluctuations, and a behavior of the
Bose condensate. The obtained results can be helpful for interpreting the
lattice QCD data at small temperature and large isospin chemical potential and
the data on multiple pion production in high energy nuclear collisions.
