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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Bobak, Carly
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University of Guelph

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.

Aquaponics, Ordinary Differential Equations, Mathematical Model, Inverse Problem, Aquaculture, Computational Simulations, Invariant Orthant, ODE, Stineman Interpolation, Time Series Interpolation, Agriculture, Modelling, Hydroponics, Nitrogen Cycle, Fish, Sensitivity Analysis, Correlational Matrix, Global Analysis, Model Comparisons, SensSB, Inverse Problem with Partial Data, Toy Inverse Problem