The Development and Analysis of a System of Ordinary Di erential Equations to Examine Long-term Stability of an Aquaponic Environment

dc.contributor.advisorKunze, Herb
dc.contributor.authorBobak, Carly
dc.date.accessioned2016-08-29T14:08:07Z
dc.date.available2016-08-29T14:08:07Z
dc.date.copyright2016-08
dc.date.created2016-08-15
dc.date.issued2016-08-29
dc.degree.departmentDepartment of Mathematics and Statisticsen_US
dc.degree.grantorUniversity of Guelphen_US
dc.degree.nameMaster of Scienceen_US
dc.degree.programmeMathematics and Statisticsen_US
dc.description.abstractAquaponic agriculture is a sustainable system that uses interdependent processes. While it has been growing in popularity, relatively little mathematical and other academic research has been conducted in the practice of aquaponic agriculture. In this thesis, two systems of ordinary diff erential equations (ODEs) are developed and compared to mathematically model the population and concentration dynamics of the environment. Both models have an asymptotically stable non-trivial equilibrium, representing the inherent symbiotic relationship of the variables. Values of the parameters in the system are estimated from the literature so that simulated results can be presented to illustrate the nature of the solutions to the system. As well, a sensitivity analysis is performed in order to identify redundant parameters and highlight those which may need more reliable estimates. In an attempt to recover more reliable estimates, the inverse problem was solved for the simpler model with both manufactured and noisy real-world data.en_US
dc.description.sponsorshipNatural Sciences and Engineering Research Council of Canada
dc.identifier.urihttp://hdl.handle.net/10214/9902
dc.language.isoenen_US
dc.publisherUniversity of Guelphen_US
dc.rightsAttribution-ShareAlike 2.5 Canada*
dc.rights.urihttp://creativecommons.org/licenses/by-sa/2.5/ca/*
dc.subjectAquaponicsen_US
dc.subjectOrdinary Differential Equationsen_US
dc.subjectMathematical Modelen_US
dc.subjectInverse Problemen_US
dc.subjectAquacultureen_US
dc.subjectComputational Simulationsen_US
dc.subjectInvariant Orthanten_US
dc.subjectODEen_US
dc.subjectStineman Interpolationen_US
dc.subjectTime Series Interpolationen_US
dc.subjectAgricultureen_US
dc.subjectModellingen_US
dc.subjectHydroponicsen_US
dc.subjectNitrogen Cycleen_US
dc.subjectFishen_US
dc.subjectSensitivity Analysisen_US
dc.subjectCorrelational Matrixen_US
dc.subjectGlobal Analysisen_US
dc.subjectModel Comparisonsen_US
dc.subjectSensSBen_US
dc.subjectInverse Problem with Partial Dataen_US
dc.subjectToy Inverse Problemen_US
dc.titleThe Development and Analysis of a System of Ordinary Di erential Equations to Examine Long-term Stability of an Aquaponic Environmenten_US
dc.typeThesisen_US

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