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The logistic equation is often considered as a simplification of thechemostat (Kooi, Boer, Kooijman (1998)). However, the global qualitativeproperties of the delayed single species chemostat are completely known, see e.g. Smith (2011). Such properties still remain open for the delayed logisticequation, see e. g. B{\'{a}}nheley, Czendes, Kristin, and Neymaier (2014)despite that they have been announced a long time ago (Wright (1955)). We maytherefore ask whether the logistic equation really is a simplification and whatinformation about the chemostat actually is contained. We discuss the linksbetween these equations and conclude that they are less clear in the delayedcase than they are in the non-delayed case. We keep the presentation aselementary as possible.

Relationships between the delayed chemostat and the delayed logistic equation