The most basic version of a Lotka-Volterra equation captures the complex interaction between one predator and one prey population. Multidimensional Lotka-Volterra systems can capture the dynamics of large food webs. Many existing studies have used these systems to explore food webs using computer simulations. This project aims to rigorously analyze these multidimensional Lotka-Volterra models using mathematical methods. Specifically, we will use graph theory and dynamical systems techniques to answer questions like (1) why does stability break down when there are more links in the food web? and (2) does stability always deteriorate as species are added to the food web?
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Experience with linear algebra required. Experience with ODEs and coding skills in Matlab (or similar) preferred.