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