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The Cusp Catastrophe in the Urban Retail Model

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  • J F Kaashoek
  • A C F Vorst

Abstract

In this paper we will show that for a suitable choice of the parameters in an urban retail model as developed by Huff and by Lakshmanen and Hansen one finds a cusp catastrophe in the surface of equilibrium points. We give some economic consequences of the fact that we have a cusp catastrophe. Furthermore, we show that for other choices of the parameters the equilibrium points of the model depend smoothly on the parameters.

Suggested Citation

  • J F Kaashoek & A C F Vorst, 1984. "The Cusp Catastrophe in the Urban Retail Model," Environment and Planning A, , vol. 16(7), pages 851-862, July.
    • Handle: RePEc:sae:envira:v:16:y:1984:i:7:p:851-862
    DOI: 10.1068/a160851
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    Cited by:

    1. R Crouchley, 1987. "An Examination of the Equivalence of Three Alternative Mechanisms for Establishing the Equilibrium Solutions of the Production-Constrained Spatial Interaction Model," Environment and Planning A, , vol. 19(7), pages 861-874, July.
    2. P Nijkamp & A Reggiani, 1988. "Dynamic Spatial Interaction Models: New Directions," Environment and Planning A, , vol. 20(11), pages 1449-1460, November.

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