| Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 12, Iss. 1, Jan, 2008, pp. 29-53 @2008 Society for Chaos Theory in Psychology & Life Sciences Dynamics of a Discrete Population Model for Extinction and Sustainability in Ancient Civilizations Abstract: We analyze a discrete version of a recently developed ratio
dependent population-resource model. This model has been used to study
the decline of the human and resource populations on Easter Island and
the chaotic dynamics of moose and wolf populations in Canada. The dynamical
system exhibits a rich behavior of fractal basins of attraction and a
Neimark-Sacker bifurcation route to chaos. The model consists of a
coupled pair of logistic equations, with the carrying capacity for
the predators proportional to the number of prey. Keywords: nonlinear dynamics, bifurcations, Easter Island |