The model of an unstirred chemostat is generalized to that of a chemostat w
ith time-dependent input/washout rates. The novelty of the new model is tha
t time periodicity appears in the boundary conditions. The asymptotic dynam
ics of the competition between two microbial populations is determined in t
erms of the corresponding period map, which is shown to preserve the standa
rd competitive ordering. It is shown that the dynamics of competition is si
milar to that of a chemostat with constant boundary conditions. Simple crit
eria for coexistence versus competitive exclusion are presented.