Numerical Simulations of the Dynamics of Vortex Rossby Waves on a Beta-Plane

Abstract

Aquaponic agriculture is a sustainable system which uses interdependent processes and has been growing in popularity. However, relatively little mathemat- ical and other academic research has been conducted in the practice. In this paper, we develop a system of ordinary differential equations to model the population and concentration dynamics of the environment. Our model has an asymptotically stable non-trivial equilibrium, representing the inherent symbiotic relationship of the variables. Values of the nine parameters in the system are estimated from the research literature. We provide simulated results simulated results to illustrate the nature of solutions to the system, and we present and discuss a sensitivity analysis.