The operation of a periodically forced chemostat (CSTR) in which two microbial populations compete for the same nutrient has been examined. Easily implemented criteria for the stability of the resulting cycles have been obtained, using the Floquet stability theory. After examining several possibilities it was found that stable periodic trajectories of coexistence can be achieved: (a) when the dilution rate of the chemostat is properly varied in a periodic manner between two values so chosen that the growth of one population is favored by the first and the growth of the other population is favored by the second, (b) when a certain percentage of biomass and growing medium is harvested periodically from the chemostat, and (c) when both the dilution rate and the concentration of the substrate in the feed are varied simultaneously and in a periodic manner.
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