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Abstract
In this paper a possible environment is modelled as a chemostat with an input and output flow at a rate v and with a fixed nutrient concentration in the input flow. Three state variables are introduced: the nutrient concentration in the environment and the concentration of two competing species. One species is efficient at low nutrient concentration, the other one at high nutrient concentration. The possibility of coexistence is mathematically proved when a periodic step variation is imposed to the flow v.