Modeling Complex Spatial Dynamics of Two-Population Interaction in Urbanization Process

摘要

This paper is mainly devoted to lay an empirical foundation for further researching into 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 with logistic growth mathematically. The numerical simulation 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 the nonlinear interaction unbeknown to us. The results from this research are revealing for students to understand urbanization, urban-rural population interaction, chaotic dynamics, and geographical systems as complex spatial systems.