Numerical bifurcation analysis of ecosystems in a spatially homogeneous environment
Kooi, B. W. 2003. Numerical bifurcation analysis of ecosystems in a spatially homogeneous environmentActa Biotheoretica 51: 189 - 222
Abstract
The dynamics of single populations upto 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 biology processes
are considered together.