Mathematics and Statistics
Dynamics of a New Holling Type IV Predator-Prey Model
Bibi Sulaman, Vassar College ’19 and Prof. Lynn ScowThe new Holling Type IV predator-prey model was the focus of our research. This model describes a system in which the success of the predator depends on the defensiveness of the prey population, specifically on the group defense behavior. In other words, the predator becomes significantly less successful in the presence of larger numbers of prey than in smaller numbers of prey. It is important to note, however, that the model does not lead to extinction for the predator in the long term; instead, it predicts that the predator population will hover around a specific non-zero density. We used a program called Wolfram Mathematica to conduct various qualitative analyses on the model function in order to determine what type of behavior it could describe depending on the values of the various parameters involved. We also provided possible ecological explanations for the behavior described by the mathematics. We found a Hopf Bifurcation in parameter alpha, which represents the group defense factor, and we also found a Saddle-Node Bifurcation in parameter c, which represents the positive effect of predation on the predator population.