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Virginia State University

Title: Three Species Food Chain Models

Directors: Dawit Haile, Zhifu Xie

Dates of Program: June 9 - July 21, 2014

Summary:

In population dynamics, the predator-prey system has been extensively studied and the analysis of food chains is an active research area in the biomathematical science. In this project, we will focus on simple food chain models that consist of three species where the third species preys on the second one and simultaneously the second species preys on the first one. A predator is a generalist if it can change its food source in the absence of its favorite food that is very common in nature. There are several interesting cases of simple food chain models of three interacting species based on the types of predators. One such case is where there is a generalist predator and a specialist predator. Another is a case where both predators are generalists or where both are specialists.

Students will be divided into two groups and each group will investigate different food chain models. The project will combine numerical simulation and theoretical analysis on the existence of all possible solutions. Students will explore the long time behavior of the food chain models with the goal of finding the ranges of the parameters that lead different dynamics such as stable equilibrium, limit cycle, and chaos. Students are expected to conduct linear stability of equilibrium solutions. They also will be asked to conduct a two parameters analysis and to understand the interactions between the self-reproduction of prey and the self-competition of middle predator. A complete parameter graph will be produced to describe the dynamical behaviors under the interactions.

Student Researchers Supported by MAA:

James Fannie
Joilah James
Janay Joseph
Janelle Williams
Imani Wood

Student Researcher Supported by Other Sources:

Robert Benson

Program Contacts:

Lloyd Douglas
MAA NREUP
 

Support for NREUP is provided by the National Science Foundation's Division of Mathematical Sciences.

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