This model is a modification of the well-known Lotka-Volterra model of predator prey interactions. It contains two state variables x and y for the populations of predators and prey, respectively, and two parameters. The model equations are given below.

x' = x(a1 + y)

y' = y(1-x-c2y)

The parameter c2 must be positive, and the parameter a1 is negative. If the parameter c2 is set equal to zero, the Lotka-Volterra model is recovered. To understand the terms appearing in the model, first consider what happens in the absence of the predator, that is when x=0. Then the prey population follows the logistic equation

y' = y(1-c2y)

That is, the model includes a bound on the size of the prey population in the absence of predators. In the presence of predators, the growth rate of the prey population is decreased, and can even become negative if x is large enough.

The equation for the predator population has a negative growth rate in the absence of any prey. Thus the model assumes that the predators are totally dependent on the prey, and do not have a viable food source in their absence. If the population of prey is larger than -a1, then the predator population increases.

Bill Farr < bfarr@wpi.edu>
Last modified: Tue Oct 8 12:29:29 EDT 1996