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Discrete Dynamics in Nature and Society
Volume 2017 (2017), Article ID 5243287, 15 pages
https://doi.org/10.1155/2017/5243287
Research Article

A Hierarchical Allometric Scaling Analysis of Chinese Cities: 1991–2014

Department of Geography, College of Urban and Environmental Sciences, Peking University, Beijing 100871, China

Correspondence should be addressed to Jian Feng; nc.ude.ukp@naijgnef

Received 1 January 2017; Revised 22 March 2017; Accepted 9 April 2017; Published 22 May 2017

Academic Editor: Charalampos Skokos

Copyright © 2017 Yanguang Chen and Jian Feng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. Batty and P. A. Longley, Fractal Cities: A Geometry of form And Function, Academic Press, London, UK, 1994.
  2. L. Bettencourt, “The origins of scaling in cities,” American Association for the Advancement of Science. Science, vol. 340, no. 6139, pp. 1438–1441, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  3. L. M. A. Bettencourt, J. Lobo, D. Helbing, C. Kühnert, and G. B. West, “Growth, innovation, scaling, and the pace of life in cities,” Proceedings of the National Academy of Sciences of the United States of America, vol. 104, no. 17, pp. 7301–7306, 2007. View at Publisher · View at Google Scholar · View at Scopus
  4. Y. G. Chen, Fractal Urban Systems: Scaling, Symmetry, and Spatial Complexity, Science Press, Beijing, China, 2008 (Chinese).
  5. P. Frankhauser, La Fractalité des Structures Urbaines (The Fractal Aspects of Urban Structures), Economica, Paris, France, 1994.
  6. J. Lobo, L. M. A. Bettencourt, D. Strumsky, and G. B. West, “Urban scaling and the production function for cities,” PLoS ONE, vol. 8, no. 3, Article ID e58407, 2013. View at Publisher · View at Google Scholar · View at Scopus
  7. D. Rybski, S. V. Buldyrev, S. Havlin, F. Liljeros, and H. A. Makse, “Scaling laws of human interaction activity,” Proceedings of the National Academy of Sciences of the United States of America, vol. 106, no. 31, pp. 12640–12645, 2009. View at Publisher · View at Google Scholar · View at Scopus
  8. C. Carroll, “National city-size distributions: what do we know after 67 years of research?” Progress in Human Geography, vol. 6, no. 1, pp. 1–43, 1982. View at Google Scholar
  9. X. Gabaix, “Zipf's law for cities: an explanation,” Quarterly Journal of Economics, vol. 114, no. 3, pp. 739–767, 1999. View at Publisher · View at Google Scholar · View at Scopus
  10. X. Gabaix and Y. M. Ioannides, “The evolution of city size distributions,” in Handbook of Urban and Regional Economics, J. V. Henderson and J. F. Thisse, Eds., vol. 4, pp. 2341–2378, North-Holland Publishing Company, Amsterdam, Netherlands, 2004. View at Publisher · View at Google Scholar · View at Scopus
  11. P. Krugman, “Confronting the mystery of urban hierarchy,” Journal of the Japanese and International Economies, vol. 10, no. 4, pp. 399–418, 1996. View at Publisher · View at Google Scholar · View at Scopus
  12. G. K. Zipf, Human Behavior and the Principle of Least Effort, Addison-Wesley, Reading, Mass, USA, 1949.
  13. M. Batty, “The size, scale, and shape of cities,” Science, vol. 319, no. 5864, pp. 769–771, 2008. View at Publisher · View at Google Scholar · View at Scopus
  14. G. Dutton, “Foreword: size and shape in the growth of human communities,” Ekistics, vol. 36, pp. 142–243, 1973. View at Google Scholar
  15. S. Nordbeck, “Urban allometric growth,” Geografiska Annaler B, vol. 53, no. 1, pp. 54–67, 1971. View at Publisher · View at Google Scholar
  16. Y. Lee, “An allometric analysis of the US urban system: 1960–1680,” Environment and Planning A, vol. 21, no. 4, pp. 463–476, 1989. View at Publisher · View at Google Scholar · View at Scopus
  17. C. P. Lo and R. Welch, “Chinese urban population estimates,” Annals of the Association of American Geographers, vol. 67, no. 2, pp. 246–253, 1977. View at Publisher · View at Google Scholar · View at Scopus
  18. Y. Chen, “The spatial meaning of Pareto's scaling exponent of city-size distributions,” Fractals, vol. 22, no. 1-2, Article ID 14500017, 2014. View at Publisher · View at Google Scholar · View at Scopus
  19. Y. Chen, “The mathematical relationship between Zipf's law and the hierarchical scaling law,” Physica A: Statistical Mechanics and its Applications, vol. 391, no. 11, pp. 3285–3299, 2012. View at Publisher · View at Google Scholar · View at Scopus
  20. D. Pumain, Hierarchy in Natural and Social Sciences, vol. 3, Springer-Verlag, Dordrecht, Netherlands, 2006. View at Publisher · View at Google Scholar
  21. Y. Chen, “Zipf's law, hierarchical structure, and cards-shuffling model for urban development,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 480196, 21 pages, 2012. View at Publisher · View at Google Scholar
  22. G. Anderson and Y. Ge, “The size distribution of Chinese cities,” Regional Science and Urban Economics, vol. 35, no. 6, pp. 756–776, 2005. View at Publisher · View at Google Scholar · View at Scopus
  23. L. Benguigui and E. Blumenfeld-Lieberthal, “A dynamic model for city size distribution beyond Zipf 's law,” Physica A: Statistical Mechanics and its Applications, vol. 384, no. 2, pp. 613–627, 2007. View at Publisher · View at Google Scholar · View at Scopus
  24. L. Benguigui and E. Blumenfeld-Lieberthal, “Beyond the power law—a new approach to analyze city size distributions,” Computers, Environment and Urban Systems, vol. 31, no. 6, pp. 648–666, 2007. View at Publisher · View at Google Scholar · View at Scopus
  25. Y. Chen, R. Chen, N. S. Ai, and H. Q. Li, “On the fractal property of city-size distributions,” Economical Geography, vol. 13, no. 3, pp. 48–53, 1993 (Chinese).
  26. K. Gangopadhyay and B. Basu, “City size distributions for India and China,” Physica A: Statistical Mechanics and Its Applications, vol. 388, no. 13, pp. 2682–2688, 2009. View at Publisher · View at Google Scholar · View at Scopus
  27. X. Y. Ye and Y. C. Xie, “Re-examination of Zipf’s law and urban dynamics in China: a regional approach,” The Annals of Regional Science, vol. 49, no. 1, pp. 135–156, 2012. View at Google Scholar
  28. P. Bak, How Nature Works: The Science of Self-Organized Criticality, Springer, New York, NY, USA, 1997.
  29. Y. Chen, “The evolution of Zipf's law indicative of city development,” Physica A: Statistical Mechanics and Its Applications, vol. 443, pp. 555–567, 2016. View at Publisher · View at Google Scholar · View at Scopus
  30. K. Davis, “World urbanization: 1950–1970,” in Systems of Cities, I. S. Bourne and J. W. Simons, Eds., pp. 92–100, Oxford University Press, New York, NY, USA, 1978. View at Google Scholar
  31. B. Jiang and X. Yao, Geospatial Analysis and Modeling of Urban Structure and Dynamics, Springer, Berlin, Germany, 2010.
  32. M. J. Beckmann, “City hierarchies and distribution of city sizes,” Economic Development and Cultural Change, vol. 6, no. 3, pp. 243–248, 1958. View at Google Scholar
  33. M. E. J. Newman, “Power laws, Pareto distributions and Zipf's law,” Contemporary Physics, vol. 46, no. 5, pp. 323–351, 2005. View at Publisher · View at Google Scholar · View at Scopus
  34. A. Clauset, C. R. Shalizi, and M. E. Newman, “Power-law distributions in empirical data,” SIAM Review, vol. 51, no. 4, pp. 661–703, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  35. R. L. Axtell, “Zipf distribution of U.S. firm sizes,” Science, vol. 293, no. 5536, pp. 1818–1820, 2001. View at Publisher · View at Google Scholar · View at Scopus
  36. M. Batty, “Rank clocks,” Nature, vol. 444, no. 7119, pp. 592–596, 2006. View at Publisher · View at Google Scholar · View at Scopus
  37. X. Gabaix, “Zipf's law and the growth of cities,” American Economic Review, vol. 89, no. 2, pp. 129–132, 1999. View at Publisher · View at Google Scholar · View at Scopus
  38. A. Hernando, D. Puigdomènech, D. Villuendas, C. Vesperinas, and A. Plastino, “Zipf's law from a Fisher variational-principle,” Physics Letters, Section A: General, Atomic and Solid State Physics, vol. 374, no. 1, pp. 18–21, 2009. View at Publisher · View at Google Scholar · View at Scopus
  39. B. H. Hong, K. E. Lee, and J. W. Lee, “Power law in firms bankruptcy,” Physics Letters, Section A: General, Atomic and Solid State Physics, vol. 361, no. 1-2, pp. 6–8, 2007. View at Publisher · View at Google Scholar · View at Scopus
  40. B. Jiang and T. Jia, “Zipf's law for all the natural cities in the United States: a geospatial perspective,” International Journal of Geographical Information Science, vol. 25, no. 8, pp. 1269–1281, 2011. View at Publisher · View at Google Scholar · View at Scopus
  41. J. Shao, P. C. Ivanov, B. Uroević, H. E. Stanley, and B. Podobnik, “Zipf rank approach and cross-country convergence of incomes,” Europhysics Letters, vol. 94, no. 4, Article ID 48001, 2011. View at Publisher · View at Google Scholar · View at Scopus
  42. M. H. R. Stanley, S. V. Buldyrev, S. Havlin, R. N. Mantegna, M. A. Salinger, and H. E. Eugene, “Zipf plots and the size distribution of firms,” Economics Letters, vol. 49, no. 4, pp. 453–457, 1995. View at Publisher · View at Google Scholar · View at Scopus
  43. D. Pumain and F. Moriconi-Ebrard, “City size distributions and metropolisation,” GeoJournal, vol. 43, no. 4, pp. 307–314, 1997. View at Publisher · View at Google Scholar · View at Scopus
  44. M. J. Woldenberg, “An allometric analysis of urban land use in the United States,” Ekistics, vol. 36, pp. 282–290, 1973. View at Google Scholar
  45. J. Feng and Y. G. Chen, “Spatiotemporal evolution of urban form and land-use structure in Hangzhou, China: evidence from fractals,” Environment and Planning B: Planning and Design, vol. 37, no. 5, pp. 838–856, 2010. View at Publisher · View at Google Scholar · View at Scopus
  46. Y. G. Chen, “Characterizing growth and form of fractal cities with allometric scaling exponents,” Discrete Dynamics in Nature and Society, vol. 2010, Article ID 194715, 22 pages, 2010. View at Publisher · View at Google Scholar · View at Scopus
  47. Y. G. Chen, “An allometric scaling relation based on logistic growth of cities,” Chaos, Solitons and Fractals, vol. 65, pp. 65–77, 2014. View at Google Scholar
  48. H. E. Hurst, R. P. Black, and Y. M. Simaika, Long-term Storage: An Experimental Study, Constable, London, UK, 1965.
  49. J. Feder, Fractals, Plenum Press, New York, NY, USA, 1988. View at Publisher · View at Google Scholar · View at MathSciNet
  50. B. B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman and Company, New York, NY, USA, 1982.
  51. R. E. Horton, “Erosional development of streams and their drainage basins; hydrophysical approach to quantitative morphology,” Bulletin of the Geological Society of America, vol. 56, no. 3, pp. 275–370, 1945. View at Publisher · View at Google Scholar · View at Scopus
  52. I. Rodriguez-Iturbe and A. Rinaldo, Fractal River Basins: Chance and Self-Organization, Cambridge University Press, Cambridge, UK, 2001.
  53. S. A. Schumm, “Evolution of drainage systems and slopes in badlands at Perth Amboy, New Jersey,” Bulletin of the Geological Society of America, vol. 67, no. 5, pp. 597–646, 1956. View at Publisher · View at Google Scholar · View at Scopus
  54. A. N. Strahler, “Hypsometric (area-altitude) analysis of erosional topography,” Bulletin of the Geological Society of America, vol. 63, no. 11, pp. 1117–1142, 1952. View at Publisher · View at Google Scholar · View at Scopus
  55. B. Gutenberg and C. F. Richter, Seismicity of the Earth and Associated Phenomenon, Princeton University Press, Princeton, NJ, USA, 2nd edition, 1954.
  56. D. L. Turcotte, Fractals and Chaos in Geology and Geophysics, Cambridge University Press, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  57. Y. G. Chen, “Fractals and fractal dimension of systems of blood vessels: an analogy between artery trees, river networks, and urban hierarchies,” Fractal Geometry and Nonlinear Analysis in Medicine and Biology, vol. 1, pp. 26–32, 2015. View at Google Scholar
  58. Z. L. Jiang and G. C. He, “Geometrical morphology of the human coronary arteries,” Journal of Third Military Medical University, vol. 11, no. 2, pp. 85–91, 1989 (Chinese).
  59. Z. L. Jiang and G. C. He, “Geometrical morphology of coronary arteries in dog,” Chinese Journal of Anatomy, vol. 13, no. 3, pp. 236–241, 1990 (Chinese).
  60. B. Jiang and X. Liu, “Scaling of geographic space from the perspective of city and field blocks and using volunteered geographic information,” International Journal of Geographical Information Science, vol. 26, no. 2, pp. 215–229, 2011. View at Publisher · View at Google Scholar · View at Scopus
  61. Y. G. Chen and B. Jiang, “Hierarchical scaling in systems of natural cities,” https://arxiv.org/abs/1608.05770.