Chemostat Model with Periodic Nutrient Input Described by Fourier Series
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Published
Jun 10, 2020
Page:
16-27
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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.
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.
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Original Research Article
References
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Gail SK.Wolkowicz, Xiao Quang Zhao. n-species Competition in a periodic chemostat. Journal of Dierential and Integral Equations; 2012.
Herbert D, Elsworth R, Telling RC. The continuous culture of bacteria; Atheoritical and experimental study. J. Gen. Microbiol.1956;14:601-662.
Dian Li Zhao, Sanling Yuan. Break-Even concentration and periodic behaviour of Stochastic Chemostat model with Seasonal uctuation. Science Direct; 2017.
Wu-Jun Pu, Danhua Jiang, Ya Wang, Zhanbing Bai. Spatial Dynamics of Non-local delayed unstirred Chemostat with periodic input. International Journal of Bio Mathematics; 2019.
Gradshteyn IS, Ryzhik IM. Table of integrals, series, and products. 7th Edition, Elsevier Academic press publications; 2007.
Zhao Xiao-Qiang. Dynamical systems in population Biology Springer-Verlag, New York; 2003.
Naomi Ziv, Nathan J. Brandict, David Gresham. The use of Chemostats in microbial Biology.
J.Vis Exp; 2013.
Milos Legnar, David R. McMillen, Dennis G. Cvitkovitch. Role of Dilution rate and Nutrient availability in the formation of Microbial Biolms. Front MicroBiol; 2019.
Anna Johanson, Anisha Goel, Lisbeth Olssona, Carl Johan Franzen. Respiratory physiology of Lactococcus Lactis in Chemostat Cultures and its eect on cellular Robustness in Frozen and Freeze-Dried starter cultures. Applied and Environmental Microbiology; 2020.
Zhiyuan Li, Bo Liu, Sophia Hsin-Jung Li, Christopher G. King, Zemer Gitai, Ned S. Wingreen.
Modelling Microbial Metabolic Trade-Os in a Chemostat; 2019. BioRXiuv George Butler, Hsu SB, Paul Watman. A mathematical model of the Chemostat with periodic washout rate. SIAM J. Appl. Math; 1985.
SB. A competition model for a seasonally uctuating nutrient. Journal of Mathematical
Biology; 1980.
Gail SK.Wolkowicz, Xiao Quang Zhao. n-species Competition in a periodic chemostat. Journal of Dierential and Integral Equations; 2012.
Herbert D, Elsworth R, Telling RC. The continuous culture of bacteria; Atheoritical and experimental study. J. Gen. Microbiol.1956;14:601-662.
Dian Li Zhao, Sanling Yuan. Break-Even concentration and periodic behaviour of Stochastic Chemostat model with Seasonal uctuation. Science Direct; 2017.
Wu-Jun Pu, Danhua Jiang, Ya Wang, Zhanbing Bai. Spatial Dynamics of Non-local delayed unstirred Chemostat with periodic input. International Journal of Bio Mathematics; 2019.
Gradshteyn IS, Ryzhik IM. Table of integrals, series, and products. 7th Edition, Elsevier Academic press publications; 2007.