A system of ODE's is considered as a model of two populations competing for a nutrient, where nutrient inputs and chemostat washouts are periodic. As well, general nutrient uptake functions which may also be time dependent and periodic are considered. Criteria are derived for there to exist a globally attracting positive periodic solution, and a theorem on global monotonicity of attracting solutions between different systems is proved.
Journal of mathematical analysis and applications, Vol. 249, no. 2 (Sept. 2000), pp. 330-323