Bifurcation analysis of a product inhibition model of a continuous fermentation process

Lenbury, Yongwimon; Chiaranai, Chalard

doi:10.1007/bf00252012

Cited by 8 publications

(1 citation statement)

References 7 publications

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“…In their two papers, Lenbury and Chiaranai (7,8) considered the case where the growth limiting substrate is supplied in sufficient amount so that S>> KS at any moment and the concentration change of S has little effect on dX/dT and dP/dT. The above system was reduced to the following two-variable system.…”

Section: Methodsmentioning

confidence: 99%

On the stability of periodic solutions for a product inhibition model of continuous biological reactors.

Lenbury

Punpocha

1989

J. Gen. Appl. Microbiol.

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A three-variable product-inhibition model of a continuous fermentation process is considered. It is shown that as time progresses all solution trajectories in the three-dimension solution space approach a plane and thus the three-variable system is equivalent to a model involving only two variables. With this result, we are able to obtain the stability condition for limit cycles bifurcating from a non-washout steady state of the three-variable model, and at the same time rule out the possibility of developing chaotic trajectories through subsequent bifurcations.Oscillatory behavior frequently occurs in both batch and continuous fermentation processes (6,14). In batch cell growth data, we often observe what appears to be random deviations about a smooth exponentially increasing function. For most design and control applications such a smoothed function describes the system adequately. However, scaleup from the small batch fermentor to large commercial batch and continuous reactors utilizing microorganisms is still very much an art. As Tanner suggested in his recent work (14), part of the difficulty in scaling up is perhaps directly attributable to the neglect of such small deviations in the process of designing the large vessel. He further stated that if small irregularities in the cell growth were not just random deviation from a smoothed function, then they must be reproducible, lead to recognizable patterns, and ultimately make sense in terms of the underlying biochemical events among the growing microorganisms.Attempts along this line have been made by Lenbury et al. (9,11) who showed that the yield expression must depend on both the cell and substrate levels for oscillations to occur in both the substrate and the cell concentrations.With continuous fermentation, on the other hand, oscillations in the ex-* Address reprint requests to:

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Section: Methodsmentioning

confidence: 99%

On the stability of periodic solutions for a product inhibition model of continuous biological reactors.

Lenbury

Punpocha

1989

J. Gen. Appl. Microbiol.

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Oscillations in continuous cultures of microorganisms: Criteria of utility of mathematical models

Ivanitskaya¹,

Petrikevich²,

Bazykin³

1989

Biotech & Bioengineering

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This article proposes a new approach to the modeling of continuous cultures of microorganisms based on the concept of universality classes. Instead of analysis of concrete sets of equations, vast classes including models with identical qualitative features should be studied. The class of models of the second order is the simplest one, and it is analyzed in order to demonstrate the mathematical methods used. The authors have shown that the simplest model usually used for the description of continuous cultures is sensitive to even slight modifications. The modified model changes its properties and gives rise to a class of models that are applicable to the description of damped and nondamped oscillations of biomass and substrate concentrations in a fermenter. Irrespective of the mode of the initial model modification, the oscillations have a number of common features. These features can be used as the criteria of utility of this class of models for simulation of culture behavior. Two models of the class in question (with nonzero maintenance coefficient and nonconstant yield) are analyzed using these criteria.

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Oscillatory behavior of population density in continuous culture of genetic‐engineered Bacillus stearothermophilus

Koizumi

Aiba

1989

Biotech & Bioengineering

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An oscillatory behavior in population density was observed when a transformant of Bacillus stearothermophilus carrying a rocombinant plasmid pZAM26 was cultivated continuously in a well-stirred reactor vessel at a fixed dilution rato. Among the transformant cells that were subjected to the continuous culture, the fraction of cells harboring p2AM26 was found to be as high as 0.98-1.00 despite the emergence of the oscillation. Cells whose plasmids underwent rearrangement of DMA in terms of structural change could not be found throughout. With reference to this observation, the dynamics of the genetic-engineered bacterium was analyzed within the category of both the linearized stability principle and the bifurcation theory. It was concluded that Hopf bifurcation was most probable to account for the experimental oscillation.

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Bifurcation analysis of a product inhibition model of a continuous fermentation process

Cited by 8 publications

References 7 publications

On the stability of periodic solutions for a product inhibition model of continuous biological reactors.

On the stability of periodic solutions for a product inhibition model of continuous biological reactors.

Oscillations in continuous cultures of microorganisms: Criteria of utility of mathematical models

Oscillatory behavior of population density in continuous culture of genetic‐engineered Bacillus stearothermophilus

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