Global Dynamics of a Chemostat Competition Model with Distributed Delay

We study the global dynamics of n-species competition in a chemo-stat with distributed delay describing the time-lag involved in the conversion of nutrient to viable biomass. The delay phenomenon is modelled by the gamma distribution. The linear chain trick and a uctuation lemma are applied to obtain the global limiting behavior of the model. When each population can survive if it is cultured alone, we prove that at most one competitor survives. The winner is the population that has the smallest delayed break-even concentration, provided that the orders of the delay kernels are large and the mean delays modiied to include the washout rate (which we call the virtual mean delays) are bounded and close to each other, or the delay kernels modiied to include the washout factor (which we call the virtual delay kernels) are close in L 1-norm. Also, when the virtual mean delays are relatively small, it is shown that the predictions of the distributed delay model are identical with the predictions of the corresponding ODEs model without delay. However, since the delayed break-even concentrations are functions of the parameters appearing in the delay kernels, if the delays are suu-ciently large, the prediction of which competitor survives, given by the ODEs model, can diier from that given by the delay model.