ABSTRACT
In an earlier paper a very general model for population growth and migration processes was introduced. In terms of population growth and migration theory for a system of urban places, the configuration of constants in the matrix, can be arranged to produce almost any system of population flows that is desired. Because most available theory about city sizes argues that a hierarchy and gradation of sizes having a particular frequency distribution is to be expected, there is little theoretical interest in devising migration models that would ‘flatten’ this distribution. This chapter considers properties of an urban-system migration process that may be developed from the theory of linear systems of ordinary differential equations. One question of particular interest for population geography concerns what kinds of population growth and migration flows result from the imposition of certain rules on the system.
