Description
Pulley, Lucas C. 2011. Analyzing Predator-Prey Models Using Systems of Ordinary Linear Differential Equations. Southern Illinois Universitiy, Honors Theses. Paper 344.
See https://opensiuc.lib.siu.edu/cgi/viewcontent.cgi?article=1349&context=uhp_theses . Accessed 29 March 2023.
Abstract: The main operating concern of all species in any ecosystem or natural environment is rooted in the battle for survival. This constant battle for survival is most highlighted in the two main modes of species interaction; categorized as predation or competition. This research focused on applying biological mathematics to analyzing predation relationships, especially the relationship between the Canadian Lynx and the Snowshoe Hare. This predation relationship is quite special, because these species interact in a relatively isolated manner compared to others, meaning their populations fluctuated in a regular cycle due to lack of significant external variables on the relationship. These population fluctuations can be defined and analyzed mathematically using systems of linear ordinary differential equations, built of course upon several minimizing assumptions in order to exclude incalculable variables. This mathematical model, the Lotka-Volterra, can then be analyzed analytically or using computer simulation to determine period lengths, phase portraits, critical points, and other practical information to the reality of the relationship. Ability to analyze and predict such relationships can be quite useful in the biology field when studying extinction based on predation, or even excessive coevolution based on population interaction.
Keywords: differential equation, models, nonlinear, predator prey, Lotka-Volterra, simulations, critical values
2011-Lucas_Pulley.pdf
Comments
Comments
There are no comments on this resource.