Numerical bifurcation analysis of ecosystems in a spatially homogeneous environment

The dynamics of single populations up to ecosystems, are often described by one or a set of non-linear ordinary differential equations. In this paper we review the use of bifurcation theory to analyse these non-linear dynamical systems. Bifurcation analysis gives regimes in the parameter space with...

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Veröffentlicht in:Acta biotheoretica 2003-01, Vol.51 (3), p.189-222
1. Verfasser: Kooi, B W
Format: Artikel
Sprache:eng
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Zusammenfassung:The dynamics of single populations up to ecosystems, are often described by one or a set of non-linear ordinary differential equations. In this paper we review the use of bifurcation theory to analyse these non-linear dynamical systems. Bifurcation analysis gives regimes in the parameter space with quantitatively different asymptotic dynamic behaviour of the system. In small-scale systems the underlying models for the populations and their interaction are simple Lotka-Volterra models or more elaborated models with more biological detail. The latter ones are more difficult to analyse, especially when the number of populations is large. Therefore for large-scale systems the Lotka-Volterra equations are still popular despite the limited realism. Various approaches are discussed in which the different time-scale of ecological and evolutionary biological processes are considered together.
ISSN:0001-5342
1572-8358
DOI:10.1023/A:1025146207201