Morphogenesis of Regional Systems

Chapter

Abstract

The most famous model of regional structure is the concentric ring model of von Thünen (1826) based on linear transportation costs, in a homogeneous plane, with a single urban market center. Subsequently this model was expanded by Christaller (1935) and Lösch (1940) to multiple market centers of different sizes and different commodities, while still assuming linear transportation costs on a homogeneous plane. For both Christaller and Lösch, the shape of a market area around a single center for a single commodity will be a hexagon. Thus the general structure of a regional hierarchy, based on a set of market areas for different commodities, will be a nested (Christaller) or overlapping (Lösch) set of hexagons.

Keywords

Entropy Migration Corn Manifold Europe 

References

  1. Allen, Peter M. and Michele Sanglier. 1981. “Urban Evolution, Self-Organization, and Decision Making.” Environment and Planning A 13, 167–183.CrossRefGoogle Scholar
  2. Alonso, William. 1978. “A Theory of Movements,” in Niles M. Hansen, ed., Human Settlement Systems. Cambridge: Ballinger, 197–211.Google Scholar
  3. Anas, Alex. 1986. “From Physical to Economic Urban Models: The Lowry Framework Revisited,” in Bruce Hutchinson and Michael Batty, eds., Advances in Urban Systems Modelling. Amsterdam: North-Holland, 163–172.Google Scholar
  4. Andersson, Åke E. 1986. “The Four Logistical Revolutions.” Papers of the Regional Science Association 59, 1–12.Google Scholar
  5. Auerbach, Felix. 1913. “Das Gesetz der Bevölkerungskonzentration.” Petermans Mitteilungen 59, 74–76.Google Scholar
  6. Batty, Michael, Paul A. Longley, and A. Stewart Fotheringham. 1989. “Urban Growth and Form: Scaling, Fractal Geometry, and Diffusion-limited Aggregation.” Environment and Planning A 21, 1447–1472.CrossRefGoogle Scholar
  7. Baumol, William J. and Jess Benhabib. 1989. “Chaos: Significance, Mechanism, and Economic Applications.” Journal of Economic Perspectives 3, 77–105.Google Scholar
  8. Beckmann, Martin J. 1952. “A Continuous Model of Transportation.” Econometrica 20, 643–660.CrossRefGoogle Scholar
  9. Beckmann, Martin J. 1953. “The Partial Equilibrium of a Continuous Space Market.” Weltwirtschaftliches Archiv 71, 73–89.Google Scholar
  10. Beckmann, Martin J. 1987. “Continuous Models of Spatial Dynamics,” in David Batten, John Casti, and Börje Johanson, eds., Economic Evolution and Structural Adjustment. Berlin: Springer, 337–348.Google Scholar
  11. Beckmann, Martin J. and Tönu Puu. 1985. Spatial Economics: Density, Potential, and Flow. Amsterdam: North-Holland.Google Scholar
  12. Booth, G. Geoffrey and Peter E. Koveos. 1983. “Employment Fluctuations: An R/S Analysis.” Journal of Regional Science 23, 19–47.CrossRefGoogle Scholar
  13. Boulding, Kenneth E. 1978. Ecodynamics: A New Theory of Societal Evolution. Beverly Hills: Sage.Google Scholar
  14. Braudel, Fernand. 1986. L’Identité de la France. Paris: Librairie Armand Colin (English translation by Reynolds, Sian, 1988, The Identity of France. New York: Harper and Row).Google Scholar
  15. Casetti, Emilio. 1980. “Equilibrium Population Partitions between Urban and Agricultural Occupations.” Geographical Analysis 12, 47–54.CrossRefGoogle Scholar
  16. Casetti, Emilio. 1982. “The Onset of Modern Economic Growth: Empirical Validation of a Catastrophe Model.” Papers of the Regional Science Association 50, 9–20.CrossRefGoogle Scholar
  17. Casti, John L. 1979. Connectivity, Complexity, and Catastrophe in Large-Scale Systems. New York: Wiley-Interscience.Google Scholar
  18. Christaller, Walter. 1933. Die Zentralen Orte in Suddendeutschland. Jena:Fischer (English translation by Baskin, C.W., 1966, Central Places in Southern Germany. Englewood Cliffs: Prentice-Hall).Google Scholar
  19. Dendrinos, Dimitrios S. 1980a. “Dynamics of City Size and Structural Stability: The Case of a Single City.” Geographical Analysis 12, 236–244.CrossRefGoogle Scholar
  20. Dendrinos, Dimitrios S. 1982. “On the Dynamic Stability of Interurban/Regional Labor and Capital Movements.” Journal of Regional Science 22, 529–540.CrossRefGoogle Scholar
  21. Dendrinos, Dimitrios S. 1984a. “Regions, Antiregions, and their Dynamic Stability: The U.S. Case (1929–1979).” Journal of Regional Science 24, 65–83.CrossRefGoogle Scholar
  22. Dendrinos, Dimitrios S. 1984b. “The Structural Stability of the US Regions: Evidence and Theoretical Underpinnings.” Environment and Planning A 16, 1433–1443.CrossRefGoogle Scholar
  23. Dendrinos, Dimitrios S. 1985. “Turbulence and Fundamental Urban/Regional Dynamics.” Task Force on Dynamic Analysis of Spatial Development, IIASA, Laxenburg, Austria.Google Scholar
  24. Dendrinos, Dimitrios S. 1989. “Growth Patterns of the Eight Regions in the People’s Republic of China (1980–1985).” Annals of Regional Science 23, 213–222.CrossRefGoogle Scholar
  25. Forrester, Jay W. 1969. Urban Dynamics. Cambridge: MIT Press.Google Scholar
  26. Fotheringham, A. Stewart, Michael Batty, and Paul A. Longley. 1989. “Diffusion-Limited Aggregation and the Fractal Nature of Urban Growth.” Papers of the Regional Science Association 67, 55–69.CrossRefGoogle Scholar
  27. Garreau, Joel R. 1981. The Nine Nations of North America. New York: Avon.Google Scholar
  28. Geddes, Patrick. 1915. Cities in Evolution. London: Williams and Norgate.Google Scholar
  29. Goodwin, Richard M. 1951. “The Nonlinear Accelerator and the Persistence of Business Cycles.” Econometrica 19, 1–17.CrossRefGoogle Scholar
  30. Goodwin, Richard M. 1967. “A Growth Cycle,” in C.H. Feinstein, ed., Socialism, Capitalism and Economic Growth. Cambridge: Cambridge University Press.Google Scholar
  31. 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
  32. Hassan, R. 1972. “Islam and Urbanization in the Medieval Middle East.” Ekistics 33, 108.Google Scholar
  33. Hicks, John R. 1950. A Contribution to the Theory of the Trade Cycle. Oxford: Oxford University Press.Google Scholar
  34. Jantsch, Erich. 1979. The Self-Organizing Universe: Scientific and Human Implications of the Emerging Paradigm of Evolution. Oxford: Pergaman Press.Google Scholar
  35. Jantsch, Erich. 1982. “From Self-Reference to Self-Transcendence: The Evolution of Self-Organization Dynamics,” in William C. Schieve and Allen, Peter M., eds., Self-Organization and Dissipative Structures. Austin: University of Texas Press, 344–353.Google Scholar
  36. Koopmans, Tjalling C. 1949. “Optimum Utilization of Transportation Systems.” Econometrica 17, 136–146.CrossRefGoogle Scholar
  37. Lösch, August. 1940. Die Raumlich Ordnumg der Wirtschaft. Jena: Fischer (English translation by Woglom, W.G., 1954, The Economics of Location. New Haven: Yale University Press).Google Scholar
  38. Lotka, Alfred J. 1920. “Analytical Notes on Certain Rhythmic Relations in Organic Systems.” Proceedings of the National Academy of Sciences, United States 6, 410–415.CrossRefGoogle Scholar
  39. Lowry, Ira S. 1964. A Model of Metropolis. RM-4035-RC, Rand Corporation, Santa Monica.Google Scholar
  40. Lung, Yannick. 1988. “Complexity of Spatial Dynamics Modelling. From Catastrophe Theory to Self Organizing Process: A Review of the Literature.” Annals of Regional Science 22, 81–111.CrossRefGoogle Scholar
  41. Mandelbrot, Benoit B. 1965. “Very Long-Tailed Probability Distributions and the Empirical Distribution of City Sizes,” in Fred Massarik and Philbun Ratoosh, eds., Mathematical Exploration in Behavioral Science. Homewood: L.R. Irwin, 322–332.Google Scholar
  42. Mandelbrot, Benoit B. 1969. “Long-Run Linearity, Locally Gaussian Process, H-Spectra, and Infinite Variances.” International Economic Review 10, 82–111.CrossRefGoogle Scholar
  43. Mandelbrot, Benoit B. 1972. “Statistical Methodology for Nonperiodic Cycles: From Covariance to R/S Analysis.” Annals of Economic and Social Measurement 1, 259–290.Google Scholar
  44. Mandelbrot, Benoit B. 1983. The Fractal Geometry of Nature. New York: W.H. Freeman.Google Scholar
  45. Maturana, Humberto R. and Francisco Varela. 1975. Autopoietic Systems. Report BCL 9.4. Urbana: Biological Computer Laboratory, University of Illinois.Google Scholar
  46. May, Robert M. 1976. “Simple Mathematical Models with Very Complicated Dynamics.” Nature 261, 459–467.CrossRefGoogle Scholar
  47. May, Robert M. and George F. Oster. 1976. “Bifurcating and Dynamic Complexity in Simple Ecological Models.” American Naturalist 110, 573–599.CrossRefGoogle Scholar
  48. Medio, Alfredo. 1984. “Synergetics and Dynamic Economic Models,” in Richard M. Goodwin, M. Kruger, and Alessandro Vercelli, eds., Nonlinear Models of Fluctuating Growth. Berlin: Springer, 166–191.Google Scholar
  49. Nicolis, Grégoire and Ilya Prigogine. 1977. Self-Organization in Nonequilibrium Systems: From Dissipative Structures to Order Through Fluctuations. New York: Wiley-Interscience.Google Scholar
  50. Nijkamp, Peter and Jacques Poot. 1987. “Dynamics of Generalized Spatial Interaction Models.” Regional Science and Urban Economics 17, 367–390.CrossRefGoogle Scholar
  51. Orishimo, Isao. 1987. “An Approach to Urban Dynamics.” Geographical Analysis 19, 200–210.CrossRefGoogle Scholar
  52. Papageorgiou, G.J. 1980. “On Sudden Urban Growth.” Environment and Planning A 12, 1035–1050.CrossRefGoogle Scholar
  53. Puu, Tönu. 1979. “Regional Modelling and Structural Stability.” Environment and Planning A 11, 1431–1438.CrossRefGoogle Scholar
  54. Puu, Tönu. 1981a. “Stability and Change in Two-Dimensional Flows,” in Daniel A. Griffith and R.D. MacKinnon, eds., Dynamic Spatial Models. Alphen aan den Rijn: Sitjhoff and Noordhoff, 242–255.Google Scholar
  55. Puu, Tönu. 1981b. “Structural Stability in Geographical Space.” Environment and Planning A 13, 979–989.CrossRefGoogle Scholar
  56. Puu, Tönu. 1982. “Outline of a Trade Cycle Model in Continuous Space and Time.” Geographical Analysis 14, 19.Google Scholar
  57. Puu, Tönu. 1986. “Multiple-Accelerator Models Revisited.” Regional Science and Urban Economics16, 81–95.CrossRefGoogle Scholar
  58. Puu, Tönu. 1987. “Complex Dynamics in Continuous Models of the Business Cycle,” in David Batten, John Casti, and Börje Johannson, eds., Economic Evolution and Structural Adjustment. Berlin: Springer, 227–259.Google Scholar
  59. Puu, Tönu. 1989. Nonlinear Economic Dynamics. Berlin: Springer.Google Scholar
  60. Puu, Tönu. 1990. “A Chaotic Model of the Business Cycle.” Occasional Paper Series on Socio-Spatial Dynamics 1, 1–19.Google Scholar
  61. Rogerson, Peter A. 1985. “Disequilibrium Adjustment Processes and Chaotic Dynamics.” Geographical Analysis 17, 185–198.CrossRefGoogle Scholar
  62. Rosser, J. Barkley, Jr. 1990a. “Approaches to the Analysis of the Morphogenesis of Regional Systems.” Occasional Paper Series on Socio-Spatial Dynamics 1(2), 75–102.Google Scholar
  63. Samuelson, Paul A. 1939. “Interactions between the Multiplier Analysis and the Principle of Acceleration.” Review of Economics and Statistics 21, 75–78.CrossRefGoogle Scholar
  64. Samuelson, Paul A. 1967. “A Universal Cycle?,” in R. Henn, ed., Methods of Operations Research III. Muhlgasse: Verlag Anton Hain, 170–183.Google Scholar
  65. Samuelson, Paul A. 1971. “Generalized Predator-Prey Oscillations in Ecological and Economic Equilibrium.” Proceedings of the National Academy of Sciences 68, 980–983.CrossRefGoogle Scholar
  66. Schrödinger, Erwin. 1944. What is Life? Cambridge: Cambridge University Press.Google Scholar
  67. Sheppard, Eric. 1983. “Pasinetti, Marx and Urban Accumulation Dynamics,” in Daniel A. Griffith and Anthony C. Lea, eds., Evolving Geographical Structures: Mathematical Models and Theories for Space-Time Processes. The Hague: Martinus Nijhoff, 293–322.Google Scholar
  68. Turing, Alan M. 1952. “The Chemical Basis of Morphogenesis.” Philosophical Transactions of the Royal Society B 237, 37.CrossRefGoogle Scholar
  69. van der Pol, Balthasar. 1927. “Forced Oscillations in a Circuit with Nonlinear Resistance (Receptance with Reactive Triode).” London, Edinburgh and Dublin Philosophical Magazine 3, 65–80.Google Scholar
  70. Volterra, V. 1937. “Principes de Biologia Mathématique.” Acta Biotheoretica 3, 1–36.CrossRefGoogle Scholar
  71. von Bertalanffy, Ludwig. 1962. General Systems Theory. New York: George Braziller.Google Scholar
  72. Wegener, Michael. 1982. “Modelling Urban Decline: A Multi-Level Economic-Demographic Model of the Dortmund Region.” International Regional Science Review 7, 21–41.CrossRefGoogle Scholar
  73. Wegener, Michael, Friedrich Gnad, and Michael Vannahme. 1986. “The Time Scale of Urban Change,” in Bruce Hutchinson and Michael Batty, eds., Advances in Urban Systems Modelling. Amsterdam: North-Holland, 175–198.Google Scholar
  74. White, Roger W. 1985. “Transitions to Chaos with Increasing System Complexity: The Case of Regional Industrial Systems.” Environment and Planning A 17, 387–396.CrossRefGoogle Scholar
  75. Zhang, Wei-Bin. 1988. “The Pattern Formation of an Urban System.” Geographical Analysis 20, 75–84.CrossRefGoogle Scholar
  76. Zipf, George K. 1941. National Unity and Disunity. Bloomington: Principia Press.Google Scholar
  77. 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
  78. Kantorovich, Leonid V. 1942. “On the Translocation of Masses.” Doklady Akademii Nauk SSSR 37: translated into English in Management Science 5, 1–4.Google Scholar
  79. 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
  80. Dendrinos, Dimitrios S. and Henry Mulally. 1985. Urban Evolution: Studies in the Mathematical Ecology of Cities. Oxford: Oxford University Press.Google Scholar
  81. Dendrinos, Dimitrios S. and Henry Mulally. 1981. “Evolutionaly Patterns of Urban Populations.” Geographical Analysis 13, 328–344.CrossRefGoogle Scholar
  82. Dendrinos, Dimitrios S. and Henry Mulally. 1983a. “Empirical Evidence of Volterra-Lotka Dynamics in United States Metropolitan Areas: 1940–1977,” in Griffith, Daniel A. and Lea, Anthony C., eds., Evolving Geographical Structures: Mathematical Models and Theories for Space-Time Processes. The Hague: Martinus Nijhoff, 170–195.Google Scholar
  83. Dendrinos, Dimitrios S. and Henry Mulally. 1984. “Interurban Population and Capital Accumulations and Structural Stability.” Applied Mathematics and Computation 14, 11–24.CrossRefGoogle Scholar
  84. Dendrinos, Dimitrios S. and Michael Sonis. 1987. “The Onset of Turbulence in Discrete Relative Multiple Spatial Dynamics.” Applied Mathematics and Computation 22, 25–44.CrossRefGoogle Scholar
  85. Dendrinos, Dimitrios S. and Michael Sonis. 1988. “Nonlinear Discrete Relative Population Dynamics of the U.S. Regions.” Applied Mathematics and Computation 25, 265–285.CrossRefGoogle Scholar
  86. Dendrinos, Dimitrios S. and Michael Sonis. 1989. Turbulence and Socio-Spatial Dynamics: Toward a Theory of Social Systems Evolution. Berlin: Springer.Google Scholar
  87. Dendrinos, Dimitrios S. and Michael Sonis. 1990. “Signatures of Chaos: Rules in Sequences of Spatial Stock Size Distributions for Discrete Relative Dynamics?” Occasional Paper Series on Socio-Spatial Dynamics 1, 57–73.Google Scholar
  88. Dendrinos, Dimitrios S. and Michael Sonis. 1986. “Variational Principles and Conservation Conditions in Volterra’s Ecology and in Urban Relative Dynamics.” Journal of Regional Science 26, 359–377.CrossRefGoogle Scholar
  89. Batten, David and Börje Johansson. 1987. “Dynamics of Metropolitan Change.” Geographical Analysis 19, 189–199.CrossRefGoogle Scholar
  90. Diener, Marc and Tim Poston. 1984. “The Perfect Delay Convention, or The Revolt of the Slaved Variables,” in Hermann Haken, ed., Chaos and Order in Nature, 2nd Edition. Berlin: Springer, 249–268.Google Scholar
  91. Lorenz, Hans-Walter. 1987b. “International Trade and the Possible Occurrence of Chaos.” Economics Letters 23, 135–138.CrossRefGoogle Scholar
  92. Rosser, J. Barkley, Jr. 1974. “A Review of Concepts Employed in Urban and Regional Economic Models.” Institute for Environmental Studies Working Paper 15, University of Wisconsin-Madison.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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