Qualitative analysis of system dynamics ecological models

Authors

  • Miguel Toro,

    Associate Professor
    1. Escuela Universitaria Politkcnica, Virgen de Africa 7, 41011 Sevilla, Spain
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    • Escuela Universitaria Politkcnica of the University of Seville, Spain, where he teaches computer science and systems theory. He received the Ingeniero Industrial and the Doctor Ingeniero Industrial degrees from that university. His chief research interests are in system dynamics methodology and qualitative analysis of dynamic systems.

  • Javier Aracil

    Professor
    1. Escuela Superior Ingenieres Industriales, Avda. Reina Marcedes s/n, 41012 Sevilla, Spain
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    • Escuela Superior de Ingenieros Industriales of the University of Seville, Spain, where he teaches control and systems theory. He received the Ingeniero Industrial and the Doctor Ingeniero Industrial degrees from the Universidad Politkcnica de Madrid, Spain, and is Licenciado en Informatica by the same university. He has consulted on system dynamics applications to socioeconomic planning. His current research interests are the theory of dynamic systems modeling, with emphasis on the application of qualitative methods to system dynamics models. He received the 1986 Jay W. Forrester Award for contributions in this area.


Abstract

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.

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