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Complex Dynamics in Spatial Systems

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Complex Evolutionary Dynamics in Urban-Regional and Ecologic-Economic Systems

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Abstract

Dynamic complexity is a part of a broader meta-complexity that encompasses many different definitions of complexity, with the list of 45 provided by Seth Lloyd (Horgan, 1997) being the basic starting point (Rosser, 2009a). Dynamic complexity can be seen as consisting of four categories: cybernetics, catastrophe, chaos, and interacting heterogeneous agent-based complexity, which Rosser (1999b) previously labeled “small-tent complexity,” the “big-tent complexity” being this overall dynamic complexity. However, given the vaguely insulting implication of this “small-tent” label, as well as the fact that dynamic complexity is hardly the totality of complexity, it seems better to use a more precisely descriptive term. Indeed, for many people when they hear the term “complexity,” it is often this small-tent or agent-based complexity (also sometimes labeled “Santa Fe complexity”) that they think of.

The unpurged images of day recede;

The emperor’s drunken soldiery are abed;

Night resonance recedes, night-walkers’ song

After great cathedral gong;

A starlit or a moonlit dome disdains

All that man is,

All mere complexities,

The fury and the mire of human veins.

William Butler Yeats, 1930, “Byzantium”

But evidently analysis of ‘tipping’ phenomena wherever it occurs — in neighborhoods, jobs, restaurants, universities or voting blocs — and whether it involves blacks and whites, men and women, French-speaking and English-speaking, officers and enlisted men, young and old, faculty and students, or any other dichotomy, requires explicit attention to the dynamic relationship between individual behavior and collective results.

Thomas C. Schelling (1971a, “Dynamic Models of Segregation,” p. 186).

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References

  • Andersson, Åke E. 1986. “The Four Logistical Revolutions.” Papers of the Regional Science Association 59, 1–12.

    Google Scholar 

  • Arthur, W. Brian, Steven N. Durlauf, and David A. Lane. 1997. “Introduction,” in W. Brian Arthur, Steven N. Durlauf, and David A. Lane, eds., The Economy as an Evolving Complex System II. Reading: Addison-Wesley, 1–14.

    Google Scholar 

  • Auerbach, Felix. 1913. “Das Gesetz der Bevölkerungskonzentration.” Petermans Mitteilungen 59, 74–76.

    Google Scholar 

  • Bak, Per. 1996. How Nature Works: The Science of Self-Organized Criticality. New York: Copernicus Press for Springer.

    Google Scholar 

  • Banos, Arnaud. 2010. “Network Effects in Schelling’s Model of Segregation: New Evidence from Agent-Based Simulation.” Mimeo, Géographie-Cité, CNRS, Paris.

    Google Scholar 

  • Berry, Brian J.L. 1964. “Cities as Systems within Systems of Cities.” Papers of the Regional Science Association 13, 147–163.

    Article  Google Scholar 

  • Blume, Lawrence E. 1993. “The Statistical Mechanics of Strategic Interaction.” Games and Economic Behavior 5, 387–424.

    Article  Google Scholar 

  • Blume, Lawrence E. 1997. “Population Games,” in W. Brian Arthur, Steven N. Durlauf, and David A. Lane, eds., The Economy as an Evolving Complex System II. Reading: Addison-Wesley, 425–460.

    Google Scholar 

  • Boulding, Kenneth E. 1978. Ecodynamics: A New Theory of Societal Evolution. Beverly Hills: Sage.

    Google Scholar 

  • Braudel, Fernand. 1979. Le Temps du Monde. Paris: Librairie Armand Colin (English translation by Reynolds, Sian, 1984, The Perspective of the World. New York: Harper and Row).

    Google Scholar 

  • Brock, William A. and Steven N. Durlauf. 2001a. “Discrete Choice with Social Interactions.” Review of Economic Studies 68, 235–260.

    Article  Google Scholar 

  • Brock, William A. and Steven N. Durlauf. 2002. “A Multinomial Choice Model with Neighborhood Effects.” American Economic Review, Papers and Proceedings 92, 298–303.

    Article  Google Scholar 

  • Chakrabarti, Bikas K., Anirban Chakraborti, and Arnab Chatterjee, eds. 2006. Econophysics and Sociophysics: Tends and Perspectives. Weinheim: Wiley-VCH.

    Google Scholar 

  • Childe, V. Gordon. 1936. Man Makes Himself. Harmondsworth: Penguin.

    Google Scholar 

  • Clark, William A.V. and Mark Fossett. 2008. “Understanding the Social Context of the Schelling Segregation Model.” Proceedings of the National Academy of Sciences 105, 4109–4114.

    Article  Google Scholar 

  • Dendrinos, Dimitrios S. and J. Barkley Rosser, Jr. 1992. “Fundamental Issues in Nonlinear Urban Population Dynamics Models: Theory and a Synthesis.” Annals of Regional Science 26, 135–145.

    Article  Google Scholar 

  • Ellison, Glenn, Edward L. Glaeser, and Willam R. Kerr. 2010. “What Causes Industry Agglomeration? Evidence from Coagglomeration Patterns.” American Economic Review 100, 1195–1213.

    Article  Google Scholar 

  • Erdös, Paul and Joel H. Spencer. 1974. Probabilistic Methods in Combinatorics. New York: Academic Press.

    Google Scholar 

  • Estigneev, Igor V. 1988. “Stochastic Extremal Problems and the Strong Markov Property of Random Fields.” Russian Mathematical Surveys 43, 1–49.

    Article  Google Scholar 

  • Estigneev, Igor V. 1991. “Controlled Random Fields on Graphs and Stochastic Models of Economic Equilibrium,” in V.V. Sazonov and T. Shervidze, eds., New Trends in Probability and Statistics. Utrecht: VSP, 391–412.

    Google Scholar 

  • Fagiolo, Giorgio, Marco Valente, and Nicolaas J. Vriend. 2007. “Segregation in Networks.” Journal of Economic Behavior and Organizaion 64, 316–336.

    Article  Google Scholar 

  • Foster, Dean and H. Peyton Young. 1990. “Stochastic Evolutionary Game Dynamics.” Theoretical Population Biology 38, 219–232.

    Article  Google Scholar 

  • Fujita, Masahisa, Paul Krugman, and Anthony J. Venables. 2001. The Spatial Economy: Cities, Regions, and International Trade, Paperback edition. Cambridge: MIT Press.

    Google Scholar 

  • Fujita, Masahisa and Hideaki Ogawa. 1982. “Multiple Equilibria and Structural Transition of Non-Monocentric Urban Configurations.” Regional Science and Urban Economics 12, 161–196.

    Article  Google Scholar 

  • Horgan, John. 1997. The End of Science: Facing the Limits of Knowledge in the Twilight of the Scientific Age, Paperback edition. New York: Broadway Books.

    Google Scholar 

  • Ioannides, Yannis M. 1990. “Trading Uncertainty and Market Form.” International Economic Review 31, 619–638.

    Article  Google Scholar 

  • Ioannides, Yannis M. 1997. “Evolution of Trading Structures,” in W. Brian Arthur, Steven N. Durlauf, and David A. Lane, eds., The Economy as an Evolving Complex System II. Reading: Addison-Wesley, 129–167.

    Google Scholar 

  • Kirman, Alan P., Claude Oddou, and Shlomo Weber. 1986. “Stochastic Communication and Coalition Formation.” Econometrica 54, 129–138.

    Article  Google Scholar 

  • Krugman, Paul R. 1996. The Self-Organizing Economy. Cambridge: Blackwell.

    Google Scholar 

  • Laurie, Alexander J. and Narendra K. Jaggi. 2003. “The Role of ‘Vision’ in Neighborhood Racial Segregation: A Variant of the Schelling Model.” Urban Studies 40, 2687–2704.

    Article  Google Scholar 

  • 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 

  • Lotka, Alfred J. 1925. Elements of Physical Biology. Baltimore: Williams and Wilkins.

    Google Scholar 

  • Mandelbrot, Benoit B. 1963. “The Variation of Certain Speculative Prices.” Journal of Business 36, 394–419.

    Article  Google Scholar 

  • McCauley, Joseph L. 2004. Dynamics of Markets: Econophysics and Finance. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • O’Sullivan, Arthur. 2009. “Schelling’s Model Revisited: Residential Sorting with Competitive Bidding for Land.” Regional Science and Urban Economics 39, 397–408.

    Article  Google Scholar 

  • Pancs, Romans and Nicolaas J. Vriend. 2006. “Schelling’s Spatial Proximity Model of Segregation Revisited.” Journal of Public Economics 91, 1–24.

    Article  Google Scholar 

  • Papageorgiou, Y.Y. and T.R. Smith. 1983. “Agglomeration as Local Instability of Spatially Uniform Steady-States.” Econometrica 51, 1109–1119.

    Article  Google Scholar 

  • Pollicott, Mark and Howard Weiss. 2001. “The Dynamics of Schelling-Type Segregation Models and a Nonlinear Graph Laplacian Variational Problem.” Advances in Applied Mathematics 27, 17–40.

    Article  Google Scholar 

  • 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 

  • Rosser, J. Barkley, Jr. 1994. “Dynamics of Emergent Urban Hierarchy.” Chaos, Solitons & Fractals 4, 553–562.

    Article  Google Scholar 

  • Rosser, J. Barkley, Jr. 1999b. “On the Complexities of Complex Economic Dynamics.” Journal of Economic Perspectives 13(4), 169–192.

    Article  Google Scholar 

  • Rosser, J. Barkley, Jr. 2009a. “Introduction,” in J. BarkleyRosser, Jr., ed., Handbook of Research on Complexity. Cheltenham: Edward Elgar, 3–11.

    Google Scholar 

  • Rosser, J. Barkley, Jr., Carl Folke, Folke Günther, Heikki Isomäki, Charles Perrings, and Tönu Puu. 1994. “Discontinuous Change in Multilevel Hierarchical Systems.” Systems Research 11, 77–94.

    Article  Google Scholar 

  • Schelling, Thomas C. 1969. “Models of Segregation.” American Economic Review, Papers and Proceedings 59, 488–493.

    Google Scholar 

  • Schelling, Thomas C. 1971a. “Dynamic Models of Segregation.” Journal of Mathematical Sociology 1, 143–186.

    Article  Google Scholar 

  • Schelling, Thomas C. 1978. Micromotives and Macrobehavior. New York: W.W. Norton.

    Google Scholar 

  • Stauffer, Dietrich and Sorin Solomon. 2007. “Ising, Schelling and Self-Organising Segregation.” European Physical Journal B 57, 473–479.

    Article  Google Scholar 

  • Vinković, Dejan and Alan Kirman. 2006. “A Physical Analogue of the Schelling Model.” Proceedings of the National Academy of Sciences 103, 19261–19265.

    Article  Google Scholar 

  • Watts, Duncan J. 1999. Small Worlds. Princeton: Princeton University Press.

    Google Scholar 

  • Watts, Duncan J. 2003. Six Degrees: The Science of a Connected Age. New York: W.W. Norton.

    Google Scholar 

  • Watts, Duncan J. and Steven H. Strogatz. 1998. “Collective Dynamics of Small-World Networks.” Nature 393, 440–442.

    Article  Google Scholar 

  • Weidlich, Wolfgang. 2002. Sociodynamics: A Systematic Approach to the Mathematical Modelling in the Social Sciences. London: Taylor & Francis.

    Google Scholar 

  • Weidlich, Wolfgang and Günter Haag. 1987. “A Dynamic Phase Transition Model for Spatial Agglomeration Processes.” Journal of Regional Science 27, 529–569.

    Article  Google Scholar 

  • Wittfogel, Karl A. 1957. Oriental Despotism: A Comparative Study of Total Power. New Haven: Yale University Press.

    Google Scholar 

  • Young, H. Peyton. 1998. Individual Strategy and Social Structure: An Evolutionary Theory of Institutions. Princeton: Princeton University Press.

    Google Scholar 

  • Zhang, Junfu. 2004a. “A Dynamic Model of Residential Segregation.” Journal of Mathematical Sociology 28, 147–170.

    Article  Google Scholar 

  • Zipf, George K. 1941. National Unity and Disunity. Bloomington: Principia Press.

    Google Scholar 

  • Zipf, George K. 1949. Human Behavior and the Principle of Least Effort. Cambridge: Addison-Wesley.

    Google Scholar 

  • 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 

  • Dendrinos, Dimitrios S. and Henry Mulally. 1985. Urban Evolution: Studies in the Mathematical Ecology of Cities. Oxford: Oxford University Press.

    Google Scholar 

  • Dendrinos, Dimitrios S. and Henry Mulally. 1981. “Evolutionaly Patterns of Urban Populations.” Geographical Analysis 13, 328–344.

    Article  Google Scholar 

  • 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 

  • Dendrinos, Dimitrios S. and Michael Sonis. 1987. “The Onset of Turbulence in Discrete Relative Multiple Spatial Dynamics.” Applied Mathematics and Computation 22, 25–44.

    Article  Google Scholar 

  • Dendrinos, Dimitrios S. and Michael Sonis. 1988. “Nonlinear Discrete Relative Population Dynamics of the U.S. Regions.” Applied Mathematics and Computation 25, 265–285.

    Article  Google Scholar 

  • Dendrinos, Dimitrios S. and Michael Sonis. 1989. Turbulence and Socio-Spatial Dynamics: Toward a Theory of Social Systems Evolution. Berlin: Springer.

    Google Scholar 

  • 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 

  • Erdös, Paul and Alfréd Renyi. 1959. “On Random Graphs I.” Publicationes Mathematicae Debreccen 6, 290–297.

    Google Scholar 

  • Erdös, Paul and Alfréd Renyi. 1960. “On the Evolution of Random Graphs.” Publications of the Mathematical Institute of the Hungarian Academy of Sciences 5, 17–61.

    Google Scholar 

  • Barabási, Albert-László and Réka Albert. 1999. “Emergence of Scaling in Random Networks.” Science 286, 509–512.

    Article  Google Scholar 

  • 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 

  • Pareto, Vilfredo. 1897. Cours d’Économie Politique, Vol. II. Lausanne: F. Rouge

    Google Scholar 

  • Mantegna, Rosario N. and H. Eugene Stanley. 2000. An Introduction to Econophysics. Cambridge: Cambridge University Press.

    Google Scholar 

  • Yakovenko, Victor and J. Barkley Rosser, Jr. 2009. “Colloquium: Statistical Mechanics of Money, Wealth, and Income.” Reviews of Modern Physics 81, 1703–1725.

    Article  Google Scholar 

  • Singer, H.W. 1936. “The ‘Courbe des populations’: A Parallel to Pareto’s Law.” Economic Journal 46, 254–263.

    Article  Google Scholar 

  • Carroll, A.R. 1982. “National City Size Distributions: What Do We Know After 67 Years of Research?” Progress in Human Geography 6, 1–43.

    Google Scholar 

  • Gabaix, Xavier. 1999. “Zipf’s Law for Cities: An Explanation.” Quarterly Journal of Economics 114, 739–768.

    Article  Google Scholar 

  • Gibrat, R. 1931. Les Inégalités Économiques. Paris: Librairie de Recueil Sirey.

    Google Scholar 

  • Rosen, K.T. and M. Resnick. 1980. “The Size Distribution of Cities.” Journal of Urban Economics 8, 165–186.

    Article  Google Scholar 

  • Ioannides, Yannis M. and Henry G. Overman. 2003. “Zipf’s Law for Cities: An Empirical Examination.” Regional Science and Urban Economics 33, 127–137.

    Article  Google Scholar 

  • Batten, David. 2001. “Complex Landscapes of Spatial Interaction.” Annals of Regional Science 35, 81–111.

    Article  Google Scholar 

  • Dobkins, Linda H. and Yannis M. Ioannides. 2001. “Spatial Interactions among US Cities.” Regional Science and Urban Economics 31, 701–731.

    Article  Google Scholar 

  • Song, S. and K.H. Zhang. 2002. “Urbanization and City Size Distribution in China.” Urban Studies 39, 2317-2327.

    Article  Google Scholar 

  • Davis, Donald and David Weinstein. 2002. “Bones, Bombs, and Breakpoints: The Geography of Economic Activity.” American Economic Review 99, 1269–1289.

    Article  Google Scholar 

  • De Vries, J. 1984. European Urbanization 1500–1800. Cambridge: Harvard University Press.

    Google Scholar 

  • Lagopoulos, A.P. 1971. “Rank-Size and Primate Distribution in Greece.” Ekistics 32, 380–386.

    Google Scholar 

  • Krakover, S. 1998. “Testing the Turning Point Hypothesis in City-Size Distribution.” Urban Studies 35, 2183–2196.

    Article  Google Scholar 

  • Berry, Brian J.L. 2010. “The Distribution of City Sizes,” in Claudio Cioffi-Rivilla, ed., Statistical, Mathematical, and Computational Emergence in Complex Social Systems, forthcoming.

    Google Scholar 

  • 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 

  • Futagami, Koichi and Kazuo Mino. 1995. “Public Capital and Patterns of Growth in the Presence of Threshold Externalities.” Journal of Economics 61, 123–146.

    Google Scholar 

  • Rosser, J. Barkley, Jr. 1998. “Coordination and Bifurcation in Growing Spatial Economies.” Annals of Regional Science 32, 133–143

    Article  Google Scholar 

  • Lucas, Robert E., Jr. 2001. “Externalities in Cities.” Review of Economic Dynamics 4, 245–274.

    Article  Google Scholar 

  • Brulhart, Marius and Federica Sbergami. 2009. “Agglomeration and Growth: Cross-Country Evidenc.” Journal of Urban Economics 65, 48–63.

    Article  Google Scholar 

  • Nicolis, John S. 1986. Dynamics of Hierarchical Systems: An Evolutionary Approach. Berlin: Springer.

    Google Scholar 

  • Simon, Herbert A. 1955. “On a Class of Skew Distributions.” Biometrika 42, 425–445.

    Google Scholar 

  • Launhardt, Wilhelm. 1885. Mathematische Begundung der Volkswirtschaftslehre. Leipzig: B.G. Teubner

    Google Scholar 

  • Reilly, William J. 1931. The Law of Retail Gravitation. New York: Knickerbocker Press.

    Google Scholar 

  • Henderson, Vernon. 1988. Urban Development: Theory, Fact, and Illusion. New York: Oxford University Press.

    Google Scholar 

  • Cronon, William. 1991. Nature’s Metropolis: Chicago and the Great West. New York: W.W. Norton.

    Google Scholar 

  • Steward, Julian H. 1949. “Cultural Causality and the Law.” American Anthropologist 51, 1–27.

    Article  Google Scholar 

  • Butzer, K. 1976. Early Hydraulic Civilization in Egypt. Chicago: University of Chicago Press.

    Google Scholar 

  • Park, Thomas. 1992. “Early Trends toward Class Stratification: Chaos, Common Property, and Flood Recession Agriculture.” American Anthropologist 94, 90–117.

    Article  Google Scholar 

  • Allen, R.C. 1997. “Agriculture and the Origins of the State in Ancient Egypt.” Explorations in Economic History 34, 135–154.

    Article  Google Scholar 

  • Clark, William A.V. 1992. “Residential Preferences and Neighborhood Racial Segregation: A Test of the Schelling Segregation Model.” Demography 28, 1–19.

    Article  Google Scholar 

  • Epstein, Joshua M. and Robert Axtell. 1996. Growing Artificial Societies: Social Science from the Bottom Up. Washington: Brookings Institution.

    Google Scholar 

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  1. Department of Economics, James Madison University, South Main St. 800, Harrisonburg, VA, 22807, USA

    J. Barkley Rosser

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Rosser, J.B. (2011). Complex Dynamics in Spatial Systems. In: Complex Evolutionary Dynamics in Urban-Regional and Ecologic-Economic Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8828-7_5

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