P-50 Positive Solutions to a General Predator-Prey System with Combined Self-limitation and Competition

Buller Hall Lobby

The Lotka-Volterra predator-prey biological model tells us about the population dynamics in a two-species system where one of the species preys upon the other. We seek the mathematical existence of a unique positive solution to a more generalized form of the predator-prey model with homogeneous boundary conditions. Using the sub- and supersolution method, we employ the mean value theorem to see that even though one species is food for the other, a solution exists where both species can survive, giving us more insight into the nature of the limiting factors and competition between the species in the predator-prey relationship.