On the existence of chaotic behavior in simple and pure microbial competition: the role of Contois kinetics

Abdelhamid Ajbar, Mohamed Asif, Emad Ali


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 simple and pure competition when the microbial populations interact in no other way except the competition for a single rate-limiting nutrient that affects their growth rates.
The issue whether simple and pure competition under time invariant conditions can give rise to chaotic behavior has been unresolved for decades.
Recently, Ajbar~\cite{Ajbar2012} showed, for the first time, that chaos can theoretically occur in these systems by analyzing 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 behavior can occur in a much simpler model of pure and simple competition. We examine the case where only one species grows following 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 behavior of the proposed model is quite simple, the dynamic behavior is complex and involves period doubling culminating to chaos.
The proposed model could serve as a basis to re-examine the importance of Contois kinetics in predicting complex behavior in microbial competition.

doi: 10.1017/S1446181113000345


Simple and pure competition,chaos,contois model

DOI: http://dx.doi.org/10.21914/anziamj.v55i0.6267

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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.