A DYNAMIC PHASE TRANSITION MODEL FOR SPATIAL AGGLOMERATION PROCESSES*

Abstract

A nonlinear model of population migration is presented in order to provide a dynamic explanation for the formation of metropolitan areas. "In Section 2 the model is introduced in terms of the rate equations for the mean values of the regional population numbers with specifically chosen individual transition rates. Section 3 gives a survey of concepts and results for the convenience of the reader not interested in the details of the mathematical derivations. Section 4 derives the stationary solutions of the rate equations, that is, the equilibria of the system. Section 5 treats the time dependent solutions of the model equations focussing on the exact analytic solutions along so-called symmetry paths. Section 6 analyzes the dynamic stability of the symmetry path solutions and decides which stationary states are unstable and which are stable equilibrium states."