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| van Coller, Lynn; UBC; lvcoller@nbs.co.za. |
| 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... |
| Tipo: Peer-Reviewed Reports |
Palavras-chave: Bifurcation; Computer analysis; Dynamical systems; Ecological models; Qualitative analysis; Ratio-dependent model; XPPAUT.. |
| Ano: 1997 |
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| Scheffer, Marten; Wageningen Agricultural University; Marten.Scheffer@wur.nl. |
| Despite the huge scientific progress of the last century, the dynamics of complex systems such as the atmosphere, human societies, and ecosystems remain difficult to understand and predict. Nonetheless, our ability to carve the future depends largely on our insight into the functioning of such complex systems. Complex systems are the focus of considerable mathematical theory. Rather than referring to any particular part of the world, such theory addresses what seems to be another world: a world of strange attractors, catastrophe folds, torus destruction, and homoclinic bifurcations. So disparate is the language and notation in this discipline that it is hard to imagine that it has any thing to do with reality as we know it. Indeed, it deals with a kind of... |
| Tipo: Peer-Reviewed Reports |
Palavras-chave: Bifurcation; Catastrophe; Chaos; Cycle; Daphnia; Fish; Macrophyte; Model; Multiple stable states; Plankton; Predation; Trophic cascade. |
| Ano: 1999 |
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