Date of Award
5-2020
Degree Type
Honors College Thesis
Department
Mathematics
First Advisor
Zhifu Xie, Ph.D.
Advisor Department
Mathematics
Abstract
In this paper, the classical Lotka-Volterra model is expanded based on functional response of Holling type III to analyze a dynamical predator-prey relationship with hunting cooperation (a) and the Allee effect among predators. The stability of equilibrium solutions was first analyzed by deriving a Jacobian matrix from partial derivatives of our model. Newly derived eigenvalues are then used to determine the stability. The viability of the model is then demonstrated by using MATLAB. The numerical results show a clear Allee effect and a variety of possible phenomena related to stability when carrying capacity (k) is varied. Two different types of bifurcations are then observed from our numerical results.
Copyright
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Recommended Citation
McGee, Regen S., "The Long Time Behavior of the Predator-Prey Model with Holling Type III" (2020). Honors Theses. 727.
https://aquila.usm.edu/honors_theses/727