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 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.
Kooi
B W
BW
Department of Theoretical Biology, Institute of Ecological Science, Faculty of Earth and Life Sciences, Vrije Universiteit, de Boelelaan 1087, 1081 HV Amsterdam, The Netherlands. kooi@bio.vu.nl
D000818:Animals; D005075:Biological Evolution; D017753:Ecosystem; D020387:Food Chain; D008954:Models, Biological; D017711:Nonlinear Dynamics; D009716:Numerical Analysis, Computer-Assisted; D011157:Population Dynamics; D011235:Predatory Behavior; D013997:Time Factors