This paper first proposes a nonlinear dynamic migration model that describes the population dynamics of cities in a region. Second, by use of this model, several theorems are proved about the conditions necessary for (1) a state of simultaneous growth (that is, when the population of every city in a region increases simultaneously), and (2) a state of proportional growth (that is, when every city's proportion of the total population remains the same over time). Third, based upon the data analysis of interprefectural migration flows in Japan in 1970, some empirical implications of these theorems are considered.
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