BIFURCATION PHENOMENA IN SOME SINGULARLY PERTURBED PHYTOPLANKTON GROWTH MODELS.

Persistent Link:
http://hdl.handle.net/10150/186093
Title:
BIFURCATION PHENOMENA IN SOME SINGULARLY PERTURBED PHYTOPLANKTON GROWTH MODELS.
Author:
KEMPF, JAMES ALBERT.
Issue Date:
1983
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
Dynamical systems theory and bifurcation are used to analyze some simple models of nutrient limited phytoplankton growth. The models are restricted to batch culture type conditions allowing the use of a mass balance constraint. Two popular models from the literature, the Michaelis-Menton-Monod or M³ model, and the Droop internal nutrient model are analyzed and found to yield unreasonable predictions for certain ambient environmental conditions. The M³ model predicts that the population size becomes unbounded at equilibrium for certain values of the parameters. The Droop model predicts that the amount of nutrient left over during a nutrient uptake experiment would be very small, regardless of how large the initial external nutrient concentration is. Numerical comparisons of data with the predictions from both models demonstrate that the conditions for unreasonable behavior could occur both in cultures and in natural aquatic ecosystems. In the predicted nutrient concentration at uptake equilibrium is several orders of magnitude off. Two specific enzyme mechanisms for nutrient transport are proposed as alternatives to current models. The models differ in the assumptions made about how the backflow reaction with the enzymes responsible for transport proceeds. A nutrient uptake equation for each model is derived directly from the enzyme kinetics, while the equation for growth in population size is taken from the Droop model. The dynamics of both models are analyzed, treating the nutrient uptake equations with the singular perturbation assumption. The simple model predicts that the external nutrient concentration at uptake equilibrium should be a constant percentage of the internal concentration, while in the inhibition uptake model, the population size could exhibit relaxation type oscillations during the batch culture steady state. Qualitative evidence supporting both models is discussed. Applications of these models to water quality simulation and implications for theoretical ecology are discussed.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Phytoplankton populations -- Mathematical models.; Bifurcation theory.; Aquatic ecology -- Mathematical models.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Systems and Industrial Engineering; Graduate College
Degree Grantor:
University of Arizona

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleBIFURCATION PHENOMENA IN SOME SINGULARLY PERTURBED PHYTOPLANKTON GROWTH MODELS.en_US
dc.creatorKEMPF, JAMES ALBERT.en_US
dc.contributor.authorKEMPF, JAMES ALBERT.en_US
dc.date.issued1983en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractDynamical systems theory and bifurcation are used to analyze some simple models of nutrient limited phytoplankton growth. The models are restricted to batch culture type conditions allowing the use of a mass balance constraint. Two popular models from the literature, the Michaelis-Menton-Monod or M³ model, and the Droop internal nutrient model are analyzed and found to yield unreasonable predictions for certain ambient environmental conditions. The M³ model predicts that the population size becomes unbounded at equilibrium for certain values of the parameters. The Droop model predicts that the amount of nutrient left over during a nutrient uptake experiment would be very small, regardless of how large the initial external nutrient concentration is. Numerical comparisons of data with the predictions from both models demonstrate that the conditions for unreasonable behavior could occur both in cultures and in natural aquatic ecosystems. In the predicted nutrient concentration at uptake equilibrium is several orders of magnitude off. Two specific enzyme mechanisms for nutrient transport are proposed as alternatives to current models. The models differ in the assumptions made about how the backflow reaction with the enzymes responsible for transport proceeds. A nutrient uptake equation for each model is derived directly from the enzyme kinetics, while the equation for growth in population size is taken from the Droop model. The dynamics of both models are analyzed, treating the nutrient uptake equations with the singular perturbation assumption. The simple model predicts that the external nutrient concentration at uptake equilibrium should be a constant percentage of the internal concentration, while in the inhibition uptake model, the population size could exhibit relaxation type oscillations during the batch culture steady state. Qualitative evidence supporting both models is discussed. Applications of these models to water quality simulation and implications for theoretical ecology are discussed.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectPhytoplankton populations -- Mathematical models.en_US
dc.subjectBifurcation theory.en_US
dc.subjectAquatic ecology -- Mathematical models.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineSystems and Industrial Engineeringen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.identifier.proquest8315289en_US
dc.identifier.oclc688638983en_US
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