  In this paper, we study the minimal Keller-Segel model with a logistic source
and obtain quantitative and qualitative descriptions of the competition between
logistic damping and other ingredient, especially, chemotactic aggregation to
guarantee boundedness and convergence. More specifically, we establish how
precisely strong a logistic source can prevent blow-up, and then we obtain an
explicit relationship between logistic damping and other ingredient,
especially, chemotactic aggregation so that convergences are ensured and their
respective convergence rates are explicitly calculated out. Known results in
the literature are completed and refined.
  Furthermore, our findings provide clues on how to produce blowup solutions
for KS chemotaxis models with logistic sources.
