Delayed Nutrient Conversion for a Single Species Periodic Chemostat
Jane Ireri *
Catholic University of Eastern Africa, P.O. Box 62157-00200, Nairobi, Kenya.
Ganesh Pokhariyal
University of Nairobi, P.O. Box 30197-00200, Nairobi, Kenya.
Stephene Moindi
University of Nairobi, P.O. Box 30197-00200, Nairobi, Kenya.
*Author to whom correspondence should be addressed.
Abstract
In this paper we analyze a Chemostat model with periodic nutrient input modelled using Fourier series and incorporate delays in nutrient conversion. We show that both periodicity and delays have complementing influence in the long term behaviour of the species. Numerical results show that periodicity has bigger influence on species density variations for delays below the Hopf Bifurcation point, while for delays above the Bifurcation point,the delay effect is more influential.
Keywords: DDE, Periodic Chemostat, Fourier series, Hopf Bifurcation