This model deals with a predator-prey system. It predicts stable stationary coexistence of both populations if the rate coefficient a1 for the decline of the predator in the absence of the prey and the coefficient c2 which determines the maximum prey population (= 1/c2) in the absence of the predator satisfy the relation

0 > a1c2 > -1

If a1c2 < -1, then the stable stationary state is extinction of the predator population. This makes some biological sense. If the predators die off too quickly, or the sustainable prey population in the absence of predators is too small, then the predators die off and only the prey remain. On the other hand, there is some evidence that the populations of predator and prey oscillate, and this model, except when it becomes the Lotka-Volterra model for c2=0, does not oscillate. A better model should be able to exhibit both kinds of behavior.

Bill Farr < bfarr@wpi.edu>
Last modified: Tue Oct 8 12:34:50 EDT 1996