title: 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."
authors.forename: W
authors.initials: W
authors.lastname: Weidlich
authors.forename: G
authors.initials: G
authors.lastname: Haag
mesh_terms: D003710:Demography; D004641:Emigration and Immigration; D005843:Geography; D008962:Models, Theoretical; D011153:Population; D011154:Population Characteristics; D011157:Population Dynamics; D012106:Research; D014505:Urban Population; D014507:Urbanization
keywords: Demographic Factors; Geographic Factors; Migration; Models, Theoretical; Population; Population Characteristics; Population Dynamics; Research Methodology; Rural-urban Migration; Spatial Distribution; Urban Population; Urban Spatial Distribution--changes; Urbanization; World