Chemostat Model with Periodic Nutrient Input Described by Fourier Series
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 present a periodic Chemostat model of two species competing for a single nutrient available in limiting supply. The nutrient input is varied periodically using a Fourier series function to take into account the changing patterns as seasons vary. We show both analytically and numerically that varying the nutrient input using a Fourier Series function results in a better model to describe coexistence of species in natural environments.
Keywords: Coexistence, competition, Competitive exclusion, periodic chemostat, fourier series, stability.