# Introduction

This report is on the modified Predator-Prey model, a coupled system of differential equations. The main focus of this report is to examine the behavior of the two different populations as we vary the value of the three constants in the model. These three constants however must be postive. In our analysis of this model we will first find the fixed points and determine their stability. Then we will investigate non-hyperbolic fixed points and the periodic behavior of the model. We will show qualitative mathematical results as well as the maple and xrk programs to grapically represent the model.

The rest of our report will be structured as follows:

Backgound: Details and Explanation of the model

Analysis: Mathematical Work and Graphs

Conclusion: Summary of Results

Matthew Hirsch igel@wpi.edu

Matthew Shaw shaw@wpi.edu