Self-limitation in a discrete predator-prey model

We study the ecological and mathematical significance of a nonlinear discrete predator–prey model that includes several types of self-limitation on the prey. The model is derived for the dynamics of two interacting populations where predators feed only on prey of a certain age. We show how the introduction of different limitation factors can account for several important phenomena that affect the dynamic output of the models. We show why some of these factors contribute to a viable interaction between the two populations and some other factors originate unstable behavior with unbounded oscillations. c © 2007 Elsevier Ltd. All rights reserved.