Title

Dynamics of a model three species predator-prey system with choice

Date of Award

2007

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Center for Science and Math Education

First Advisor

Sherry Herron

Advisor Department

Center for Science and Math Education

Abstract

Studies of predator-prey systems vary from simple Lotka-Volterra type to nonlinear systems involving the Hölling Type II or Honing 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.