Abstract
Phenomena exhibiting discontinuous change, divergent processes, and hysteresis can be modelled with catastrophe theory, a recent development in differential topology. Exposition of the theory is illustrated by qualitative interpretations of the appearance of functions in central place systems, and of price cycles for urban housing.
Keywords
- Central Place
- Market Area
- Catastrophe Theory
- Property Price
- Lower Sheet
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Literature Cited
AMSON, J. "Equilibrium Models of Cities: 1 — An Axiomatic Theory," Environment and Planning, 4 (1972), 429–44.
BELL, D. The Coming of Post-Industrial Society: A Venture in Social Forecasting, London: Heinemann, 1974.
DACEY, M.F. "The Geometry of Central Place Theory," Geografiska Annaler 47B: 2 (1965), 111–24.
JONES, D.D. "The Application of Catastrophe Theory to Biological Systems," paper presented at Systems Ecological Conference, Logan, Utah, 20–23 February 1975.
KAHN, H. and A.J. WIENER, The Year 2000, New York: MacMillan, 1967.
THOM, R. "Topological Models in Biology," Topology, 8 (1969), 313–35.
THOM, R. Stabilité Structurelle et Morphogenèse, Reading, Massachusetts: Addison-Wesley, 1972.
WASSERMAN, G. Stability of Unfoldings, Springer Lecture Notes in Math, Vol. 393, New York: Springer-Verlag, 1974.
WOODSTOCK, A.E.R. and T. POSTON, A Geometrical Study of the Elementary Catastrophes, Springer Lecture Notes in Math, vol. 373, New York: Springer-Verlag, 1974.
ZEEMAN, E.C. "Differential Equations for the Heartbeat and Nerve Impulse," in C. WADDINGTON, ed., Towards a Theoretical Biology, 4, Edinburgh University Press, 1972.
ZEEMAN, E.C. "Applications of Catastrophe Theory," Mathematics Institute, University of Warwick, March, 1973.
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Casti, J., Swain, H. (1976). Catastrophe theory and urban processes. In: Cea, J. (eds) Optimization Techniques Modeling and Optimization in the Service of Man Part 1. Optimization Techniques 1975. Lecture Notes in Computer Science, vol 40. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-07622-0_483
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DOI: https://doi.org/10.1007/3-540-07622-0_483
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