Abstract
The articulation of new methods for analyzing the dynamics of spatial systems is a welcome development. Of all the weaknesses in conventional methods, the inadequacy of the treatment of time has been the most glaring. The adoption of the mathematics of nonlinearity has helped us to address some old problems in novel ways and it has opened up some important new lines of inquiry. However, some of the ways in which nonlinear dynamics has been incorporated into spatial analysis has, in my view, failed to resolve the key problems associated with producing satisfactory theories of spatial dynamics and may even have exacerbated them. I will argue that older approaches, which seem to have been largely forgotten, provide better stems than most of the currently dominant approaches on which to graft the methods of nonlinear mathematics.. In particular, I will advocate the redevelopment of ideas associated with recursive programming. They appear to offer the opportunity to elaborate new theories without the restrictions attendant on the use of what I will refer to as the planning-model strategy.
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References
Allen, P. M., & Sanglier, M., 1981, Urban Evolution, Self-organisation, and Decision-making, Environment and Planning A, 13, pp. 167–184.
Anas, A., 1984, Discrete Choice Theory and the General Equilibrium of Employment, Housing, and Travel Networks in a Lowry-type Model of the Urban Economy, Environment and Planning A, 16, pp. 1489–1502.
Anas, A., 1987, Modelling in Urban and Regional Economics, Chur: Harwood Academic.
Batty, M., P. Longley, & S. Fotheringham, 1989, Urban Growth and Form: Scaling, Fractal Geometry, and Diffusion-limited Aggregation, Environment and Planning A, 21, pp. 1447–1472.
Clarke, M., & A.G. Wilson, 1985, The Dynamics of Urban Spatial Structure - the Progress of a Research-Program, Transactions, Institute of British Geographers, 10(4), 427–451.
Day, R.H., & T. Groves, 1975, Adaptive Economic Models, Academic Press, New York.
Day, R.H., & E.H. Tinney, 1969, A Dynamic von Thünen Model, Geographical Analysis, 1, pp. 137–151.
Dendrinos, D. & H. Mullally, 1985, Urban Evolution: Studies in the Mathematical Ecology of Cities, Oxford University Press, Oxford.
Forrester, J.W., 1969, Urban Dynamics, MIT Press, Cambridge, Mass.
Harris, B., 1985, Synthetic Geography: The Nature of our Understanding of Cities, Environment and Planning A, 17, pp. 443–464.
Harris, B. & A.G. Wilson, 1978, Equilibrium Values and Dynamics of Attractiveness Terms in Production-constrained Spatial-interaction Models, Environment and Planning A, 10, pp. 371–388.
King, A.T., 1977, Computing General Equilibrium Prices for Spatial Economies, The Review of Economics and Statistics, 59, pp. 340–350.
Koopmans, T.C. & M.J. Beckmann, 1957, Assignment Problems and the Location of Economic Activities, Econometrica, 1, pp. 53–76.
Kuenne, R.E., 1992, The Economics of Oligopolistic Competition, Blackwells, Oxford.
Marris, R., 1991, Reconstructing Keynesian Economics with Imperfect Competition: a desktop simulation, Edward Elgar, Aldershot.
Mills, E.S., 1974, Mathematical Models for Urban Planning, (A. Brown et al., eds.), Urban and Social Economics in Market and Planned Economies, Praeger, New York.
Murphy, R.E. Jr., 1965, Adaptive Processes in Economic Systems, Academic Press, New York.
Nijkamp, P., & A. Reggiani, 1988, Analysis of Dynamic Spatial Interaction Models by Means of Optimal Control, Geographical Analysis, 20, pp. 18–29.
Reggiani, A., 1990, Spatial Interaction Models: New Directions, Ph.D., Vrije Universiteit, Amsterdam.
Takayama, T. & G. Judge, 1971, Spatial and Temporal Price and Allocation Models, North Holland, Amsterdam.
Williams, H.C.W.L., 1977, On the Formation of Travel Demand Models and Economic Evaluation Measures of User Benefit, Environment and Planning A, 9 pp. 285–344.
Wilson, A. G. & Birkin, M., 1987, Dynamic-models of Agricultural Location in a Spatial Interaction Framework, Geographical Analysis, 19, pp. 31–56.
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Macmillan, W.D. (1993). Microeconomics and the Dynamic Modelling of Spatial Systems. In: Nijkamp, P., Reggiani, A. (eds) Nonlinear Evolution of Spatial Economic Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-78463-7_7
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DOI: https://doi.org/10.1007/978-3-642-78463-7_7
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