  This paper is mainly devoted to lay an empirical foundation for further
research on complex spatial dynamics of two-population interaction. Based on
the US population census data, a rural and urban population interaction model
is developed. Subsequently a logistic equation on percentage urban is derived
from the urbanization model so that spatial interaction can be connected
mathematically with logistic growth. The numerical experiment by using the
discretized urban-rural population interaction model of urbanization shows a
period-doubling bifurcation and chaotic behavior, which is identical in
patterns to those from the simple mathematical models of logistic growth in
ecology. This suggests that the complicated dynamics of logistic growth may
come from some kind of the nonlinear interaction. The results from this study
help to understand urbanization, urban-rural population interaction, chaotic
dynamics, and spatial complexity of geographical systems.
