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A Mathematical Model of Segregation Patterns in Residential Neighbourhoods

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  • Hezi Yizhaq

    (Department of Solar Energy and Environmental Physics, Jacob Blaustein Institute for Desert Research, Ben-Gurion University of the Negev, Sede-Boker Campus 84990, Israel and Department of Physics, Ben-Gurion University, Beer Sheva 84105 Israel)

  • Boris A Portnov

    (Department of Natural Resources and Environmental Management, Faculty of Social Sciences, University of Haifa, Mount Carmel, Haifa, 31905 Israel, Israel)

  • Ehud Meron

    (Department of Solar Energy and Environmental Physics, Jacob Blaustein Institute for Desert Research, Ben-Gurion University of the Negev, Sede-Boker Campus 84990, Israel and Department of Physics, Ben-Gurion University, Beer Sheva 84105 Israel)

Abstract

A mathematical model is proposed which describes the dynamics and the spatial distributions of two population groups, where migration is driven by considerations of socioeconomic status. The model associates segregation with instabilities of spatially uniform mixed population states. These instabilities lead to a wide range of segregation forms including: (a) variable (weak) segregation where the population is everywhere mixed and the spatial variability is controlled by a ‘status-gap’ parameter, (b) strong segregation, where nearby neighbourhoods consists of pure (unmixed) population groups, and (c) intermediate forms involving enclaves of a pure population group in neighbourhoods of mixed population. The model associates tipping-point phenomena with the existence of an unstable mixed population state which introduces a threshold for population inversion. The model predicts that uneven invasions of one population group into another may result from interface instabilities rather than from urban heterogeneities.

Suggested Citation

  • Hezi Yizhaq & Boris A Portnov & Ehud Meron, 2004. "A Mathematical Model of Segregation Patterns in Residential Neighbourhoods," Environment and Planning A, , vol. 36(1), pages 149-172, January.
    • Handle: RePEc:sae:envira:v:36:y:2004:i:1:p:149-172
    DOI: 10.1068/a35274
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    References listed on IDEAS

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    2. Gambino, G. & Lombardo, M.C. & Sammartino, M., 2012. "Turing instability and traveling fronts for a nonlinear reaction–diffusion system with cross-diffusion," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(6), pages 1112-1132.

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