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.
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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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