Date of Award

Summer 8-2007

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Center for Science and Math Education

Committee Chair

Dr. Sherry Herron

Committee Chair Department

Center for Science and Math Education

Committee Member 2

Dr. Louis Romero

Committee Member 3

Dr. Joseph Kolibal

Committee Member 4

Dr. Myron Henry

Committee Member 5

Dr. Haiyan Tian

Committee Member 6

Dr. Robert Diehl

Abstract

Studies of predator-prey systems vary from simple Lotka-Volterra type to nonlinear systems involving the Holling Type II or Holling Type III functional response functions. Some systems are modeled to represent a simple food chain, while others involve mutualism, competition and even switching of predator-prey roles. In this study, we investigate the dynamics of a three species system in which the principle predator has a choice of two prey, while the prey species change their behavior from being prey to predator and vice versa.

Biological and mathematical conditions for the existence of equilibria and local stability are given. A proof to show the nonexistence of periodic solutions in the corresponding two species system is also given. Global stability of the coexistence equilibrium in the top predator-prey system is demonstrated through numerical simulations. The resulting quintic polynomial through full symmetry analysis provide for conditions for a cusp bifurcation using resultants theory. Various numerical simulations to illustrate the population dynamics of the corresponding two species system as well as the three species system model are given.

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