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

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dc.contributor.advisor Kunze, Herb
dc.contributor.author Bobak, Carly
dc.date.accessioned 2016-08-29T14:08:07Z
dc.date.available 2016-08-29T14:08:07Z
dc.date.copyright 2016-08
dc.date.created 2016-08-15
dc.date.issued 2016-08-29
dc.identifier.uri http://hdl.handle.net/10214/9902
dc.description.abstract Aquaponic 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.sponsorship NSERC en_US
dc.language.iso en en_US
dc.rights Attribution-ShareAlike 2.5 Canada *
dc.rights.uri http://creativecommons.org/licenses/by-sa/2.5/ca/ *
dc.subject Aquaponics en_US
dc.subject Ordinary Differential Equations en_US
dc.subject Mathematical Model en_US
dc.subject Inverse Problem en_US
dc.subject Aquaculture en_US
dc.subject Computational Simulations en_US
dc.subject Invariant Orthant en_US
dc.subject ODE en_US
dc.subject Stineman Interpolation en_US
dc.subject Time Series Interpolation en_US
dc.subject Agriculture en_US
dc.subject Modelling en_US
dc.subject Hydroponics en_US
dc.subject Nitrogen Cycle en_US
dc.subject Fish en_US
dc.subject Sensitivity Analysis en_US
dc.subject Correlational Matrix en_US
dc.subject Global Analysis en_US
dc.subject Model Comparisons en_US
dc.subject SensSB en_US
dc.subject Inverse Problem with Partial Data en_US
dc.subject Toy Inverse Problem en_US
dc.title The Development and Analysis of a System of Ordinary Di erential Equations to Examine Long-term Stability of an Aquaponic Environment en_US
dc.type Thesis en_US
dc.degree.programme Mathematics and Statistics en_US
dc.degree.name Master of Science en_US
dc.degree.department Department of Mathematics and Statistics en_US
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