Discontinuities in Intraurban Systems

Chapter

Abstract

Historically there has been considerable unity of method in modelling the regional distribution of population and economic activities and the intraurban distribution of these. The most obvious example is that the standard neoclassical Mills–Muth model (Alonso, 1964; Mills, 1967; Muth, 1969) of intraurban land use and rent is essentially similar to the von Thünen (1826) model of land use and rent over a broader regional space.

Keywords

Migration Convection Manifold Heat Content Transportation 

References

  1. Allen, Peter M. 1978. “Dynamique des Centres Urbains.” Science et Techniques 50, 15–19.Google Scholar
  2. Allen, Peter M. 1983. “Self-Organization and Evolution in Urban Systems,” in Robert W. Crosby, ed., Cities and Regions as Nonlinear Decision Systems. Boulder: Westview, 29–62.Google Scholar
  3. Allen, Peter M., Guy Engelen, and Michele Sanglier. 1986. “Towards a General Dynamic Model of the Spatial Evolution of Urban Systems,” in Bruce Hutchinson and Michael Batty, eds., Advances in Urban Systems Modelling. Amsterdam: North-Holland, 199–220.Google Scholar
  4. Allen, Peter M. and Michele Sanglier. 1978. “Dynamic Models of Urban Growth.” Journal of Social and Biological Structures 1, 265–280.CrossRefGoogle Scholar
  5. Allen, Peter M. and Michele Sanglier. 1979. “Dynamic Model for Growth in a Central Place System.” Geographical Analysis 11, 256–272.CrossRefGoogle Scholar
  6. Allen, Peter M. and Michele Sanglier. 1981. “Urban Evolution, Self-Organization, and Decision Making.” Environment and Planning A 13, 167–183.CrossRefGoogle Scholar
  7. Alonso, William. 1964. Location and Land Use. Cambridge: Harvard University Press.Google Scholar
  8. Amson, J.C. 1974. “Equilibrium and Catastrophic Models of Urban Growth,” in E.L. Cripps, ed., London Papers in Regional Science 4: Space-Time Concepts in Urban and Regional Models. Londong: Pion, 108–128.Google Scholar
  9. Amson, J.C. 1975. “Catastrophe Theory: A Contribution to the Study of Urban Systems?” Environment and Planning B 2, 177–221.CrossRefGoogle Scholar
  10. Bailey, Martin J. 1959. “A Note on the Economics of Residential Zoning and Urban Renewal.” Land Economics 35, 288–292.CrossRefGoogle Scholar
  11. Barnes, Trevor and Eric Sheppard. 1984. “Technical Choice and Reswitching in Space Economies.” Regional Science and Urban Economics 14, 345–352.CrossRefGoogle Scholar
  12. Beaumont, J.R., M. Clarke, and A.G. Wilson. 1981a. “The Dynamics of Urban Spatial Structure: Some Exploratory Results Using Difference Equations and Bifurcation Theory.” Environment and Planning A 13, 1472–1483.Google Scholar
  13. Berry, Brian J.L. 1976. “Ghetto Expansion and Single Family Housing Prices: Chicago 1968–1972.” Journal of Urban Economics 3, 397–423.CrossRefGoogle Scholar
  14. Biely, Andrey. 1913. St. Petersbeurg (English translation by Cournos, John, 1959, New York: Grove Press).Google Scholar
  15. Blase, J.H. 1979. “Hysteresis and Catastrophe Theory: Empirical Identification in Transportation Modelling.” Environment and Planning A 11, 675–688.CrossRefGoogle Scholar
  16. Boyce, Ronald R. 1963. “Myth and Reality in Urban Planning.” Land Economics 39, 241–251.CrossRefGoogle Scholar
  17. Brueckner, J.K. 1980a. “Residential Succession and Land-Use Dynamics in a Vintage Model of Urban Housing.” Regional Science and Urban Economics 10, 225–240.CrossRefGoogle Scholar
  18. Brueckner, J.K. 1981a. “A Dynamic Model of Housing Production.” Journal of Urban Economics 8, 1–14.CrossRefGoogle Scholar
  19. Brueckner, J.K. 1981b. “Testing a Vintage Model of Urban Growth.” Journal of Regional Science 12, 197–210.Google Scholar
  20. Brueckner, J.K. 1982. “Building Ages and Urban Growth.” Regional Science and Urban Economics 10, 1–17.Google Scholar
  21. Brueckner, J.K. and B. von Rabenau. 1980. “Dynamics of Land Use for a Closed City.” Regional Science and Urban Economics 10, 1–17.CrossRefGoogle Scholar
  22. Burgess, Ernest W. 1925. “The Growth of the City,” in E.W. Burgess and R.E. Park, eds., The City. Chicago: University of Chicago Press, 47–62.Google Scholar
  23. Camagni, Roberto, Lidia Diappi, and Giorgio Leonardi. 1986. “Urban Growth and Decline in a Hierarchical System.” Regional Science and Urban Economics 16, 145–160.CrossRefGoogle Scholar
  24. Coelho, José D. and Alan G. Wilson. 1976. “The Optimum Size and Location of Shopping Centers.” Regional Studies 10, 413–421.CrossRefGoogle Scholar
  25. Crank, J. 1974. “Chemical and Biological Problems,” in J.R. Ockenden and E.A. Hodgkins, eds., Moving Boundary Problems in Heat Flow and Diffusion. Oxford: Oxford University Press, 62–70.Google Scholar
  26. Dendrinos, Dimitrios S. 1978. “Urban Dynamics and Urban Cycles.” Environment and Planning A 10, 43–49.CrossRefGoogle Scholar
  27. Dendrinos, Dimitrios S. 1979. “Slums in Capitalist Urban Settings: Some Insights from DDCatastrophe Theory.” Geographia Polonica 42, 63–75.Google Scholar
  28. Dendrinos, Dimitrios S. 1981. “Individual Lot and Neighborhood Competitive Equilibria: Some Extensions from the Theory of Structural Stability.” Journal of Regional Science 21, 37–49.CrossRefGoogle Scholar
  29. Domanski, R. and A.P. Wierzbiecki. 1983. “Self-Organization in Dynamic Settlement Systems.” Papers of the Regional Science Association 51, 141–160.CrossRefGoogle Scholar
  30. Duncan, A.D. and B. Duncan. 1957. The Negro Population of Chicago. Chicago: University of Chicago Press.Google Scholar
  31. Edelson, Noel M. 1975. “The Developer’s Problem, or How to Divide a Piece of Land Most Profitably.” Journal of Urban Economics 2, 349–365.CrossRefGoogle Scholar
  32. Eggleton, R.P. 1974. “Astrophysical Problems: A Moving Boundary Probliem in the Study of Stellar Interiors,” in J.R. Ockenden and E.A. Hodgkins, eds., Moving Boundary Problems in Heat Flow and Diffusion. Oxford: Oxford University Press, 103–111.Google Scholar
  33. Fujita, Masahisa. 1976a. “Towards a Dynamic Theory of Urban Land Use.” Papers of the Regional Science Association 37, 133–165.CrossRefGoogle Scholar
  34. Fujita, Masahisa and Hideaki Ogawa. 1982. “Multiple Equilibria and Structural Transition of Non-Monocentric Urban Configurations.” Regional Science and Urban Economics 12, 161–196.CrossRefGoogle Scholar
  35. Goodwin, Philip B. 1977. “Habit and Hysteresis in Mode Choice.” Urban Studies 14, 95–98.CrossRefGoogle Scholar
  36. Haag, Günter and Dimitrios S. Dendrinos. 1983. “Toward a Stochastic Dynamical Theory of Location: A Nonlinear Migration Process.” Geographical Analysis 15, 269–286.CrossRefGoogle Scholar
  37. Haag, Günter and Wolfgang Weidlich. 1983. “A Non-Linear Dynamic Model for the Migration of Human Populations,” in Daniel A. Griffith and Anthony C. Lea, eds., Evolving Geographical Structures: Mathematical Models and Theories for Space-Time Processes. The Hague: Martunus Nijhoff, 24–61.Google Scholar
  38. Harris, B., J.M. Choukroun, and A.G. Wilson. 1982. “Economics of Scale and the Existence of Supply Side Equilibria in a Production Constrained Spatial Interaction Model.” Environment and Planning A 14, 823–837.CrossRefGoogle Scholar
  39. Harris, B. and A.G. Wilson. 1978. “Equilibrium Values and Dynamics of Attractiveness Terms in Production-Constrained Spatial-Interaction Models.” Environment and Planning A 10, 371–388.CrossRefGoogle Scholar
  40. Harris, Chauncy D. and Edward L. Ullman. 1945. “The Nature of Cities.” Annals of the American Academy of Political and Social Science 242, 7–17.CrossRefGoogle Scholar
  41. Hartwick, John. 1976. “Intermediate Goods and the Spatial Integration of Land Uses.” Regional Science and Urban Economics 6, 127–145.CrossRefGoogle Scholar
  42. Heikkila, E., P. Gordon, J.I. Kim, R.B. Peiser, H.W. Richardson, and D. Dale-Johnson. 1989. “What Happened to the CBD-Distance Gradient?: Land Values in a Policentric City.” Environment and Planning A 21, 221–232.CrossRefGoogle Scholar
  43. Hoyt, Homer. 1939. Structure and Growth of Residential Neighborhoods. Washington: Federal Housing Administration.Google Scholar
  44. Huff, D. 1964. “Defining and Estimating a Trading Area.” Journal of Marketing 28, 34–38.CrossRefGoogle Scholar
  45. Isard, Walter. 1977. “Strategic Elements of a Theory of Major Structural Change.” Papers of the Regional Science Association 38, 1–14.CrossRefGoogle Scholar
  46. Lakshmanen, T.R. and W.G. Hansen. 1965. “A Retail Potential Model.” Journal of the American Institute of Planners 31, 134–143.CrossRefGoogle Scholar
  47. Lessinger, Jack. 1962. “The Case for Scatteration: Some Reflections of the National Capital Regional Plan for the Year 2000.” Journal of the American Institute of Planners 24, 159–169.CrossRefGoogle Scholar
  48. Leung, Yee. 1987. “On the Imprecision of Boundaries.” Geographical Analysis 19, 125–151.CrossRefGoogle Scholar
  49. Lewis, D. 1977. “Public Transport and Traffic Levels.” Journal of Transport Economics and Policy 11, 155–168.Google Scholar
  50. Loury, Glenn C. 1978. “The Minimum Border Length Hypothesis Does Not Explain the Shape of Black Ghettos.” Journal of Urban Economics 5, 147–153.CrossRefGoogle Scholar
  51. Metcalfe, J. Stanley and Ian Steedman. 1972. “Reswitching and Primary Input Use.” Economic Journal 77, 140–157.CrossRefGoogle Scholar
  52. Mills, Edwin S. 1967. “An Aggregative Model of Resource Allocation in a Metropolitan Area.” American Economic Review 57, 197–210.Google Scholar
  53. Muth, Richard F. 1969. Cities and Housing. Chicago: University of Chicago Press.Google Scholar
  54. Odland, J. 1978. “The Conditions for Multi-Center Cities.” Economic Geography 54, 234–244.CrossRefGoogle Scholar
  55. Ohls, James C. and David Pines. 1975. “Discontinuous Urban Development and Economic Efficiency.” Land Economics 51, 224–234.CrossRefGoogle Scholar
  56. O’Neill, William D. 1981. “Estimation of a Logistic Growth and Diffusion Model Describing Neighborhood Change.” Geographical Analysis 13, 391–397.CrossRefGoogle Scholar
  57. Papageorgiou, Y.Y. and T.R. Smith. 1983. “Agglomeration as Local Instability of Spatially Uniform Steady-States.” Econometrica 51, 1109–1119.CrossRefGoogle Scholar
  58. Perelson, Alan S. and Evangelos A. Coutsias. 1986. “A Moving Boundary Model of Acrosomal Elogation.” Journal of Mathematical Biology 23, 361–379.CrossRefGoogle Scholar
  59. Poston, Tim and Alan G. Wilson. 1977. “Facility Size vs. Distance Travelled: Urban Services and the Fold Catastrophe.” Environment and Planning A 9, 681–686.CrossRefGoogle Scholar
  60. Pumain, D., Th. Saint-Julien, and L. Sanders. 1987. “Applications of a Dynamic Urban Model.” Geographical Analysis 19, 152–166.CrossRefGoogle Scholar
  61. Richardson, Harry W. 1975. “Discontinuous Densities, Urban Spatial Structure and Growth: A New Approach.” Land Economics 51, 305–312.CrossRefGoogle Scholar
  62. Rijk, F.J.A. and A.C.F. Vorst. 1983. “Equilibrium Points in an Urban Retail Model and Their Connection with Dynamical Systems.” Regional Science and Urban Economics 13, 383–399.CrossRefGoogle Scholar
  63. Rodriguez-Bachiller, Agustin. 1986. “Discontiguous Urban Growth and the New Urban Economics: A Review.” Urban Studies 23, 79–104.CrossRefGoogle Scholar
  64. Rose-Ackerman, Susan. 1975. “Racism and Urban Structure.” Journal of Urban Economics 2, 85–103.CrossRefGoogle Scholar
  65. Rosser, J. Barkley, Jr. 1980. “The Dynamics of Ghetto Boundary Movement and Ghetto Shape.” Urban Studies 17, 235–321.CrossRefGoogle Scholar
  66. Rosser, J. Barkley, Jr. 1982. “A Catastrophe Model of White Flight.” Mimeo, James Madison Universtiy.Google Scholar
  67. Sanglier, Michelle and Peter M. Allen. 1989. “Evolutionary Models of Urban Systems: An Applicaton to the Belgian Provinces.” Environment and Planning A 21, 477–498.CrossRefGoogle Scholar
  68. Schmid, A. Allen. 1968. Converting Rural Land to Urban Uses. Baltimore: John Hopkins University Press.Google Scholar
  69. Schweizer, U. and P. Varaiya. 1977. “The Spatial Structure of Production with a Leontief Technology-II: Substitute Techniques.” Regional Science and Urban Economics 7, 293–320.CrossRefGoogle Scholar
  70. Scott, A.J. 1979. “Commodity Production and the Dynamics of Land-Use Differentiation.” Urban Studies 16, 95–104.Google Scholar
  71. Sraffa, Piero. 1960. Production of Commodities by Means of Commodities. Cambridge: Cambridge University Press.Google Scholar
  72. Steinnes, D. 1977. “Alternative Models of Neighborhood Change.” Social Forces 55, 1043–1058.CrossRefGoogle Scholar
  73. Stull, William J. 1974. “Land Use and Zoning in an Urban Economy.” American Economic Review 63, 337–347.Google Scholar
  74. Tiebout, Charles M. 1956. “The Pure Theory of Local Public Expenditures.” Journal of Political Economy 64, 416–424.CrossRefGoogle Scholar
  75. Tucotte, D.L. 1974. “Geophysical Problems with Moving Phase Change Boundaries and Heat Flow,” in J.R. Ockenden and E.A. Hodgkins, eds., Moving Boundary Problems in Heat Flow and Diffusion. Oxford: Oxford University Press, 91–120.Google Scholar
  76. van Moerbeke, P. 1974. “An Optimal Stopping Problem with Linear Reward.” Acta Mathematica 132, 111–151.CrossRefGoogle Scholar
  77. White, Michelle J. 1975. “The Effect of Zoning on the Size of Metropolitan Areas.” Journal of Urban Economics 2, 217–283.CrossRefGoogle Scholar
  78. White, Michelle J. 1977. “Urban Models of Race Discrimination.” Regional Science and Urban Economics 7, 217–232.CrossRefGoogle Scholar
  79. Wilson, Alan G. 1970. Entropy in Urban and Regional Modelling. London: Pion.Google Scholar
  80. Wilson, Alan G. 1981a. Catastrophe Theory and Bifurcations: Applications to Urban Regional Systems. London: Croom Helm.Google Scholar
  81. Wilson, Alan G. 1981b. “Some New Sources of Instability and Oscillation in Dynamic Models of Shopping Centers and other Urban Structures.” Sitemi Urbani 3, 391–401.Google Scholar
  82. Wilson, Alan G. 1982. “Criticality and Urban Retail Structure: Aspects of Catastrophe Theory and Bifurcation,” in William C. Schieve and Peter M. Allen, eds., Self-Organization and Dissipative Structures. Austin: University of Texas Press, 159–173.Google Scholar
  83. Wolf, E.P. 1963. “The Tipping Point in Socially Changing Neighborhoods.” Journal of the American Institute of Planners 29, 217–222.CrossRefGoogle Scholar
  84. Yinger, John. 1976. “Racial Prejudice and Racial Residential Segregation in an Urban Model.” Journal of Urban Economics 3, 383–396.CrossRefGoogle Scholar
  85. Yinger, John. 1979. “Estimating the Relationship between Location and the Price of Housing.” Journal of Regional Science 21, 271–289.CrossRefGoogle Scholar
  86. von Thünen, Johann Heinrich. 1826. Der Isolierte Staat in Biechiezung auf Landwirtschaft und Nationaleckonomie. Hamburg: Perthes (English translation by Wartenberg, C.M., 1966, The Isolated State. New York: Pergamon Press).Google Scholar
  87. Allen, Peter M., J.L. Denebourg, M. Sanglier, F. Boon, and A. de Palma. 1979. “Dynamic Urban Models.” Report to Department of Transportation, USA, Contract TSC-1185, Cambridge.Google Scholar
  88. Dendrinos, Dimitrios S. and Henry Mulally. 1985. Urban Evolution: Studies in the Mathematical Ecology of Cities. Oxford: Oxford University Press.Google Scholar
  89. Dendrinos, Dimitrios S. and Henry Mulally. 1981. “Evolutionaly Patterns of Urban Populations.” Geographical Analysis 13, 328–344.CrossRefGoogle Scholar
  90. Dendrinos, Dimitrios S. 1980b. “A Basic Model of Urban Dynamics Expressed as a Set of Volterra-Lotka Equations,” in Dimitrios S. Dendrinos, ed., Catastrophe Theory in Urban and Transport Analysis, Report No. DOT/RSPA/DPB-25/80/20. Washington: US Department of Transportation.Google Scholar
  91. Dendrinos, Dimitrios S. and Gunter Haag. 1984. “Toward a Stochastic Dynamical Theory of Location: Empirical Evidence.” Geographical Analysis 16, 287–300.CrossRefGoogle Scholar
  92. Courant, Paul N. and John Yinger. 1977. “On Models of Racial Prejudice and Urban Spatial Structure.” Journal of Urban Economics 4, 272–291.CrossRefGoogle Scholar
  93. Rosser, J. Barkley, Jr. 1976. “Essays Rlated to Spatial Discontinuities in Land Values at the Urban-Rural Margin.” Ph.D. Dissertation, Department of Economics, University of Wisconsin-Madison.Google Scholar
  94. Stefan, Johan. 1891. “Über die Theorie der Eisbildung im Polarmeere.” Annals of Physics and Chemistrie, 269–281.Google Scholar
  95. Rosser, J. Barkley, Jr. 1978a. “The Theory and Policy Implications of Spatial Discontinuities in Land Values.” Land Economics 54, 430–441.CrossRefGoogle Scholar
  96. Rosser, J. Barkley, Jr. 2000b. From Catastrophe to Chaos: A General Theory of Economic Discontinuities: Mathematics, Microeconomics, Macroeconomics, and Finance, 2nd Edition, Vol. I. Boston: Kluwer Academic Publishers.Google Scholar
  97. Thompson, Michael. 1979. Rubbish Theory. Oxford: Oxford University Press.Google Scholar
  98. Clarke, M. and Alan G. Wilson. 1983. “The Dynamics of Urban Spatial Structure: Progress and Problems.” Journal of Regional Science 23, 1–18.CrossRefGoogle Scholar
  99. Fujita, Masahisa. 1981. “Spatial Patterns of Urban Growth: Optimum and Market,” in Daniel A. Griffith and Ross D. MacKinnon, eds., Dynamic Spatial Models. Alphen van den Rijn: Sijthoof and Noordhoff, 404–439.Google Scholar
  100. Smolensky, Eugene, Selwyn Becker, and Harvey Molotch. 1968. “The Prisoner’s Dilemma and Ghetto Expansion.” Land Economics 44, 420–430.CrossRefGoogle Scholar
  101. Woods, R.I. 1981. “Spatiotemporal Models of Ethnic Segregation and their Implications for Housing Policy.” Environment and Planning A 13, 1415–1433.CrossRefGoogle Scholar
  102. Becker, Gary S. 1957. The Economics of Discrimination. Chicago: University of Chicago Press.Google Scholar

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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of EconomicsJames Madison UniversityHarrisonburgUSA

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