Abstract
The modeling of discontinuous change in social and economic systems is a relatively recent phenomenon prompted by the pioneering work on the mathematics of catastrophe theory by Thorn (1975). Previously, almost all research into system dynamics was based on the concept of continuous change, in which a continuous or smooth change in some independent variable is expected to produce a continuous change in a dependent variable. Catastrophe theory allows a discontinuous change in the dependent variable to be modeled. In urban and regional analysis there have been two major uses of this approach in the investigation of discontinuous urban dynamics. One is at the macro-scale and is concerned with the examination of sudden urban growth within a system of urban areas (Amson, 1974; Allen and Sanglier, 1979; Dendrinos, 1980). The other use is at the micro-scale, and is concerned with changes in retail outlets within a single urban area (Poston and Wilson, 1977; Harris and Wilson, 1978). This latter theme is the sole concern of this paper.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Allen, P., 1980, Planning and Decision Making in the Human System: Modelling Self Organization, paper presented to the NATO Advanced Research Institute, Oxford, England, September, 1980.
Allen, P., and M. Sanglier, 1979, A Dynamic Model of Growth in a Central Place System, Geographical Analysis, 11: 256–272.
Allen, P., J- Deneubourg, M. Sanglier, F. Boon, and A. de Palma, 1978, The Dynamics of Urban Evolution, vol. 2: Intraurban Evolution, final report, Washington, D. C.: U. S. Department of Transportation.
Amson, J., 1974, Equilibrium and Catastrophic Models of Urban Growth, in Space-Time Concepts in Urban and Regional Models, edited by E. Cripps, London: Pion, pp. 108–128.
Anas, A., 1983, Discrete Choice Theory, Information Theory and the Multinomial Logit and Gravity Models, Transportation Research B, 17: 13–23.
Aplin, G., 1983, Order-Neighbor Analysis, Concepts and Techniques in Modern Geography, 36, East Anglia, England: GEO Abstracts Ltd.
Beaumont, J., M. Clarke and A. Wilson, 1981a, Changing Energy Parameters and the Evolution of Urban Spatial Structure, Regional Science and Urban Economics, 11: 287–315.
Beaumont, J., M. Clarke and A. Wilson, 1981b, The Dynamics of Urban Spatial Structure: Some Exploratory Results Using Difference Equations and Bifurcation Theory, Environment and Planning A, 13: 1473–1483.
Birkin, M., M. Clarke and A. Wilson, 1984, Interacting Fields: Comprehensive Models for the Dynamical Analysis of Urban Spatial Structure Working Paper 385, School of Geography, University of Leeds.
Clarke, M., and A. Wilson, 1983, The Dynamics of Urban Spatial Structure: Progress and Problems, Journal of Regional Science, 23: 1–18.
Dendrinos, D., 1980, Catastrophe Theory in Urban and Transport Analysis, Washington, D. C.: U. S. Department of Transportation, Research and Special Programs Administration.
Domencich, T., and D. McFadden, 1975, Urban Travel Demand: A Behavioral Analysis. Amsterdam: North-Holland.
Eaton, B., and R. Lipsey, 1979, Comparison Shopping and the Clustering of Homogeneous Firms, Journal of Regional Science, 19: 421–435.
Feigenbaum, M., 1980, Universal Behavior in Nonlinear Systems, Los Alamos Science, Summer: 4–27.
Fotheringham, A., 1983, A New Set of Spatial Interaction Models: The Theory of Competing Destination, Environment and Planning A, 15: 15–36.
Fotheringham, A., 1984, Spatial Flows and Spatial Patterns, Environment and Planning A, 16: 529–543.
Fotheringham, A., 1985, Spatial Competition and Agglomeration in Urban Modelling, Environment and Planning A, 17: 213–230.
Fotheringham, A., 1986, Modeling Hierarchical Destination Choice, Environment and Planning A, forthcoming
Fotheringham, A., and D. Knudsen, 1984, Critical Parameter Values in Retail Shopping Models, Modeling and Simulation, 15 (Part 1): 75–80.
Fotheringham, A., and D. Knudsen, 1985, Discontinuous Change in the Relative Location of Retail Outlets: Further Results, Modeling and Simulation, 16 (Part 1): 111–115.
Harris, B., and A. Wilson, 1978, Equilibrium Values and Dynamics of Attractiveness Terms in Production-constrained Spatial-interaction Models, Environment and Planning A, 10: 371–388.
Hofstadter, D., 1981, Strange Attractors: Mathematical Patterns Delicately Poised Between Order and Chaos, Scientific American, 245: 22–43.
Lioukas, S., 1984, Thresholds and Transitivity in Stochastic Consumer Choice: A Multinomial Logit Analysis, Management Science, 30: 110–122.
McFadden, D., 1974, Conditional Logit Analysis of Qualitative Choice Behavior, in Frontiers in Econometrics, edited by P. Zarembka, New York: Academic Press, pp. 105–142.
Mulligan, G., 1983, Consumer Demand and Multipurpose Shopping Behavior, Geographical Analysis, 15: 76–81.
O’Kelly, M., 1981, A Model for the Demand for Retail Facilities Incorporating Multistop, Multipurpose Trips, Geographical Analysis, 13: 134–148.
Poston, T., and A. Wilson,1977, Facility Size Versus Distance Travelled: Urban Services and the Fold Catastrophe, Environment and Planning A, 9: 681–686.
Silk, J., 1979, Statistical Concepts in Geography, London: George Allen and Unwin.
Sobel, K., 1980, Travel Demand Forecasting by Using the Nested Multinomial Logit Model, Transportation Research Record, 775: 48–55.
Thill, J., 1985, Demand in Space and Multipurpose Shopping: A Theoretical Approach, Geographical Analysis, 17: 114–129.
Thom, R., 1975, Structural Stability and Morphogensis, Reading, Mass.: Benjamin.
Tye, W., L. Sherman, M. Kinnucan, D. Nelson and T. Tardiff, 1982, Application of Disaggregate Travel Demand Models, Report 253, Washington, D. C.: Transportation Research Board, National Cooperative Highway Program.
Williams, H., 1977, On the Formulation of Travel Demand Models and Economic Evaluation Measures of User Benefit, Environment and Planning A, 9: 285–344.
Wilson, A., 1971, A Family of Spatial Interaction Models, and Associated Developments, Environment and Planning, 3: 1–32.
Wilson, A., 1981a, Oscillation in Dynamic Models of Shopping Centres and Other Urban Structures, Sistemi Urbani, 3: 391–401.
Wilson, A., 1981b, Catastrophe Theory and Bifurcation, London: Croom Helm.
Wilson, A., 1983, Making Urban Models More Realistic: Some Strategies for Future Research, WP 358, School of Geography, University of Leeds.
Wilson, A., and M. Oulton, 1983, The Corner-shop to Supermarket Transition in Retailing: The Beginnings of Empirical Evidence, Environment and Planning A, 15: 265–274.
Wrigley, N., 1985, Categorical Data Analysis for Geographers and Environmental Scientists, London: Longman.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1986 Martinus Nijhoff Publishers, Dordrecht
About this chapter
Cite this chapter
Fotheringham, A.S., Knudsen, D.C. (1986). Modeling Discontinuous Change in the Spatial Pattern of Retail Outlets: A Methodology. In: Griffith, D.A., Haining, R.P. (eds) Transformations Through Space and Time. NATO ASI Series, vol 29. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4430-5_14
Download citation
DOI: https://doi.org/10.1007/978-94-009-4430-5_14
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8472-7
Online ISBN: 978-94-009-4430-5
eBook Packages: Springer Book Archive