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A Note on the Stability of Equilibrium Solutions of Production-Constrained Spatial-Interaction Models

Author

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  • M Clarke

    (School of Geography, University of Leeds, Leeds LS2 9JT, England)

Abstract

In a recent paper an analysis of the stability of equilibrium solutions of production-constrained retailing models was undertaken by Harris and Wilson. It was argued that by examining equilibrium solutions in response to changes in a parameter, κ, jumps in the value of state variables, analogous to the fold catastrophe, could be expected. In this note it is shown that this is not necessarily always the case, and two different conditions are identified, one that gives rise to jump behaviours, and another that does not. The distinction arises from the nature of the κ parameter.

Suggested Citation

  • M Clarke, 1981. "A Note on the Stability of Equilibrium Solutions of Production-Constrained Spatial-Interaction Models," Environment and Planning A, , vol. 13(5), pages 601-604, May.
    • Handle: RePEc:sae:envira:v:13:y:1981:i:5:p:601-604
    DOI: 10.1068/a130601
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    Cited by:

    1. Minoru Osawa & Takashi Akamatsu & Yuki Takayama, 2017. "Harris And Wilson (1978) Model Revisited: The Spatial Period‐Doubling Cascade In An Urban Retail Model," Journal of Regional Science, Wiley Blackwell, vol. 57(3), pages 442-466, June.

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