A simple unforced oscillatory growth model in the chemostat.

In a chemostat, transient oscillations in cell number density are often experimentally observed during cell growth. The aim of this paper is to propose a simple autonomous model which is able to generate these oscillations, and to investigate it analytically. Our point of view is based on a simplification of the cell cycle in which there are two states (mature and immature) with the transfer between the two dependent on the available resources. We use the mathematical global properties of competitive differential systems to prove the existence of a limit cycle. A comparison between our model and a more complex model consisting of partial differential equations is made with the help of numerical simulations, giving qualitatively similar results.