Modeling Predator-Prey Interactions with ODE Systems

Systems of Ordinary Differential Equations (ODE) are a common tool used to study population dynamics. Here, we analyze a predator-prey ODE system, which models two populations in the wild, where one preys upon the other. The system also describes the Allee Effect which is key in describing species that rely on collectivist behaviors, to derive conditions for stability. We found that the stability of the system is predominantly determined by the relationship between a hyperparameter derived from the description of the predator species, and the carrying capacity of the prey population.