# Introduction

This report deals with the analysis of a two-dimensional predator-prey
model. This model is a simple modification of the well-known
Lotka-Volterra to account for finite food resources for the population
of prey, resulting in logistic behavior for the prey population in the
absence of predators. The resulting model has been scaled to contain
two parameters. The negative parameter a1 is the coefficient for
exponential decay of the predator population in the absence of prey,
and the positive parameter c2 is the reciprocal of the stable prey
population in the absence of predators.
In our analysis, we found that the trajectories always approach a
stable steady state; periodic behavior does not occur except in the
Lotka-Volterrra limit. The two types of stable steady states found
were coexistence of predator and prey populations and extinction of
the predator. As detailed later in this report, coexistence occurs
only if the inequality
0 > a1c2 > -1

is satisfied. If this inequality is not satisfied, then the predators
become extinct.
The rest of this report is organized as follows. The Background section presents the model. In
the Results section contains the details of
the analysis, and the Conclusions
section summarizes the results and criticizes the model.

Bill Farr < bfarr@wpi.edu>
Last modified: Tue Oct 8 12:30:50 EDT 1996