Global asymptotic stability and transient oscillations in delayed chemostat models
Lin Wang
Department of Mathematics and Statistics, McMaster University
Abstract
In this talk, we will first present some global asymptotic stability
results for a chemostat model with general nonmonotone response
functions and delays in the nutrient conversion process.
Under certain conditions, when n species compete in the chemostat for a
single resource that is allowed to be inhibitory at high concentrations,
even if time lags in the nutrient conversion process are taken into
consideration, our results show the competitive exclusion principle
holds. However, it is also shown that the time lags have an important
effect on the outcome of competition, and that initial condition
dependent outcome is possible. Then, by investigating a special case
(n=1), we provide an analytic method to account for the transient oscillations
observed in experiments.
