Investigations of Multidimensional Predator-Prey Models
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The Gause-Lotka-Volterra (GLV) equations are an idealized model for competition between n species. The n-RPS and May Leonard competing species models are specific cases of (GLV) which define interaction between various species differently. n-RPS couples n equations in a ?Rock-Paper-Scissors? (RPS)-type relation in which each species has both a unique predator and prey such that the n species interact with each other according to a cyclic food chain. The May-Leonard model is a three-dimensional competitive species system. Each species interacts, and negatively affects the other two species. Similar to the Logistic Model with unit carrying capacity, this effectively prevents unbounded population growth. For dimensions greater then 3, we have developed interactive graphical interfaces that numerically solve various scenarios. For 3-RPS and May-Leonard, solutions can be visualized using 3-dimensional phase portraits. For higher dimensions of n-RPS, the graphical interface plots each species populations with respect to time. Using these graphical results along with quantitative analysis we can qualitatively assess equilibrium and long-term behavior of these systems.