This article deals with the application of qualitative analysis techniques to system dynamics ecological models. Examples include the predator-prey and the Kaibab plateau models. In the former, we study the appearance of periodic motions. Bifurcation analysis allows us to determine the essential parameter that controls the appearance of the limit cycle through a Hopf bifurcation. We also study the limit case in which the model tends to be of the Lotka-Volterra type.
The Kaibab plateau model shows a collapse related to the limited availability of resources in a finite habitat. When we combine the structure of the predator-prey and Kaibab models, we obtain a model representing the chain predator-prey-food. Such a model can show a huge variety of behavior modes, including chaos, which we analyze.