Abstract

This article revisits and extends to the nonautonomous framework the results about the dynamics of a discrete and nonlinear matrix model describing the growth of a size-structured single microbial population in an autonomous chemostat, which has been introduced by T.B. Gage et.al and H.L. Smith. The first and the second result provide a threshold determining either the extinction or the persistence of the total biomass. The main result establishes a set of sufficient conditions ensuring the existence, uniqueness and global attractiveness of an omega-periodic solution.