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ON THE EXISTENCE OF CHAOTIC BEHAVIOUR IN PURE AND SIMPLE MICROBIAL COMPETITION: THE ROLE OF CONTOIS KINETICS

Part of: Mathematical biology in general Numerical problems in dynamical systems

Published online by Cambridge University Press:  21 November 2013

MOHAMMAD ASIF ,
EMAD ALI  and
ABDELHAMID AJBAR
MOHAMMAD ASIF*
Affiliation:
Department of Chemical Engineering, King Saud University, PO Box 800, Riyadh 11421, Saudi Arabia
EMAD ALI*
Affiliation:
Department of Chemical Engineering, King Saud University, PO Box 800, Riyadh 11421, Saudi Arabia
ABDELHAMID AJBAR*
Affiliation:
Department of Chemical Engineering, King Saud University, PO Box 800, Riyadh 11421, Saudi Arabia
*
✉masif@ksu.edu.sa
✉amkamal@ksu.edu.sa
✉aajbar@ksu.edu.sa
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Abstract

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Microbial competition for nutrients is a common phenomenon that occurs between species inhabiting the same environment. Bioreactors are often used for the study of microbial competition since the number and type of microbial species can be controlled, and the system can be isolated from other interactions that may occur between the competing species. A common type of competition is the so-called “pure and simple” competition, where the microbial populations interact in no other way except the competition for a single rate-limiting nutrient that affects their growth rates. The issue of whether pure and simple competition under time-invariant conditions can give rise to chaotic behaviour has been unresolved for decades. The third author recently showed, for the first time, that chaos can theoretically occur in these systems by analysing the dynamics of a model where both competing species grow following the biomass-dependent Contois model while the yield coefficients associated with the two species are substrate-dependent. In this paper we show that chaotic behaviour can occur in a much simpler model of pure and simple competition. We examine the case where only one species grows following the Contois model with variable yield coefficient while the other species is allowed to grow following the simple Monod model with constant yield. We show that while the static behaviour of the proposed model is quite simple, the dynamic behaviour is complex and involves period doubling culminating in chaos. The proposed model could serve as a basis to re-examine the importance of Contois kinetics in predicting complex behaviour in microbial competition.

Keywords

microbial competitionchemostatContois modelvariable yield coefficientcomplex behaviourchaosbifurcation

MSC classification

Secondary: 65P20: Numerical chaos 65P30: Bifurcation problems 92B05: General biology and biomathematics
Type
Research Article
Information
The ANZIAM Journal , Volume 55 , Issue 2 , October 2013 , pp. 162 - 174
Copyright
Copyright ©2013 Australian Mathematical Society 

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