The Effect of the Specific Growth Rate and Yield Expressions on the Existence of Oscillatory Behavior of a Continuous Fermentation Model

Crooke, Philip S.; Wei, Chia-Jenn; Tanner, Robert D.

doi:10.1080/00986448008912540

Cited by 78 publications

(25 citation statements)

References 5 publications

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“…The author consider a non-ideal bioreactor in which the bioreactor was divided into two regions, a well-mixed region and an unreacted region. This study showed that the variability of the substrate yield is a necessary condition for the existence of periodic behavior and it extends earlier finding of Crooke et al (1980), that showed the periodic solutions cannot occur for systems with a constant yield, from an ideal reactor to a non-ideal reactor.…”

Section: Models With a Variable Yield Coefficientsupporting

confidence: 87%

Analysis of a Chemostat Model with Variable Yield Coefficient and Substrate Inhibition: Contois Growth Kinetics

Alqahtani

Nelson

Worthy

2014

Chemical Engineering Communications

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2015, Copyright Taylor & Francis Group, LLC.We analyze the steady-state operation of a generalized reactor model that encompasses a continuous flow bioreactor and an idealized continuous flow membrane reactor as limiting cases. The biochemical reaction kinetics is governed by a Contois growth model subject to noncompetitive substrate inhibition with a variable substrate yield coefficient. The steady-state performance of the reactor is predicted and stability of the steady-state solutions as a function of dimensionless residence time reported. Our results identified two cases of practical interest. The first feature corresponds to the case where solutions to both no-washout and washout conditions are bistable. The second feature identifies the parameter region in which periodic solutions can occur when the yield coefficient is not constant. Both these features are often undesirable in practical applications and must be avoided. Scaling of the model equations reveals that both the second-bifurcation parameters are functions of the influent concentration. Our results predict how the reactor behavior varies as a function of influent concentration and identify the range of influent concentrations where the reactor displays neither periodic nor bistable behavior.

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Section: Models With a Variable Yield Coefficientsupporting

confidence: 87%

Analysis of a Chemostat Model with Variable Yield Coefficient and Substrate Inhibition: Contois Growth Kinetics

Alqahtani

Nelson

Worthy

2014

Chemical Engineering Communications

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“…Similar experiments could be performed to test the predictions using microorganisms known to have variable yields. See [1,2,5,6,18] for examples of such microorganisms.…”

Section: Discussionmentioning

confidence: 99%

“…Models with linear yields were biologically motivated by [1,5,6] who noticed the existence of limit cycles for some values of the parameters. The rigorous mathematical study was given in [18].…”

Section: Monod Growth Functions and Linear Yieldsmentioning

confidence: 99%

Competitive Exclusion for Chemostat Equations with Variable Yields

Sari¹

2012

Acta Appl Math

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“…But the accumulation of experimental data suggests that a constant yield fails to explain the observed oscillatory behavior in the chemostat [3]. Cooke [1,2] suggested a linear function for the yield coefficient and declared that a limit cycle may exist in his model. Huang [11,12] and Pilyugin and Waltman [7] constructed the model with a general variable yield, and studied the multiple limit cycles and the hopf bifurcation for the model.…”

Section: Introductionmentioning

confidence: 99%