Provider: Resilliance Alliance
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TY - JOUR
A1 - van Coller, Lynn
TI - Automated Techniques for the Qualitative Analysis of Ecological Models: Continuous Models
N2 - The mathematics required for a detailed analysis of the behavior of a model can be formidable. In this paper, I demonstrate how various computer packages can aid qualitative analyses by implementing techniques from dynamical systems theory. Because computer software is used to obtain the results, the techniques can be used by nonmathematicians as well as mathematicians. In-depth analyses of complicated models that were previously very difficult to study can now be done. Because the paper is intended as an introduction to applying the techniques to ecological models, I have included an appendix describing some of the ideas and terminology. A second appendix shows how the techniques can be applied to a fairly simple predator-prey model and establishes the reliability of the computer software. The main body of the paper discusses a ratio-dependent model. The new techniques highlight some limitations of isocline analyses in this three-dimensional setting and show that the model is structurally unstable. Another appendix describes a larger model of a sheep-pasture-hyrax-lynx system. Dynamical systems techniques are compared with a traditional sensitivity analysis and are found to give more information. As a result, an incomplete relationship in the model is highlighted. I also discuss the resilience of these models to both parameter and population perturbations.
JO - Ecology and Society
PB - The Resilience Alliance
Y1 - 1997
P1 - 1997
VL - 1
IS - 1
C7 - 5
UR - http://www.ecologyandsociety.org/vol1/iss1/art5/
DO - 10.5751/ES-00017-010105
KW - bifurcation
KW - computer analysis
KW - dynamical systems
KW - ecological models
KW - qualitative analysis
KW - ratio-dependent model
KW - XPPAUT.
ER -