Primacy analysis in the system of Bulgarian cities
The concept of "primacy" as introduced by Jefferson in 1939 in urban geography leads to the notion of "dominant city" also known as the primate city. Practically, the notion was extended by Sheppard in view of discussing some "hierarchy". The type of dominance is not universal nor any hierarchy reversal. Both can be time and sample dependent. Thus, as an example taking into consideration the existence of both pieces of the puzzle, we consider and discuss the Bulgarian urban system. It is also interesting to compare data on two groups of cities in different time intervals: (i) the whole Bulgaria city system which contains about 250 cities, - studied in the time interval between 2004 and 2011, and (ii) a system of 33 cities, - studied over the time interval 1887 till 2010. These latter cities are selected because the population was already over 10 000 inhabitants in 1946. It is shown that new additional indices are interestingly introduced in order to compensate defects in the Sheppard index. Numerical illustrations are illuminated through a "length ratio" measure, which allows to distinguish the (often) observed departures from the hyperbolic ranking seen by Jefferson.
G. Nadjakov Institute of Solid State Physics,
Bulgarian Academy of Sciences, Blvd. Tzarigradsko Chaussee 72,
BG-1784 Sofia, Bulgaria
School of Management,
University of Leicester, University Road, Leicester, LE1 7RH, UK
and e-Humanities group, Royal Netherlands Academy (NKV), Joan
Muyskenweg 25, 1096 CJ Amsterdam, The Netherlands
GRAPES, Beauvallon Res., rue de la Belle Jardiniere, 483/0021,
B-4031, Liege Angleur, Euroland
-  M. Jefferson, The Law of the Primate City, Geographical Review29(4): 226-232 (1939).[Crossref]
-  G. K. Zipf, Human Behavior and the Principle of Least Effort: AnIntroduction to Human Ecology, (Addison Wesley,Cambridge,MA, 1949).
-  H. Kantz, T. Schreiber, Nonlinear time series analysis, (CambridgeUniversity Press, Cambridge, UK, 1997).
-  N. K. Vitanov, Upper bounds on convective heat transport in arotating fluid layer of infinite Prandtl number: Case of intermediateTaylor numbers, Phys. Rev. E 62(3): 3581-3591 (2000).
-  R. Axelrod, M. D. Cohen, Harnessing complexity: Organizationalimplications on a scientific frontier, (Free Press, New York,1999).
-  T. Boeck, N. K. Vitanov, Low-dimensional chaos in zero-PrandtlnumberBenard–Marangoni convection, Phys. Rev. E 65(3):037203 (2002).
-  T. Puu, A. Panchuk, Nonlinear economic dynamics, (Springer,Berlin, 1991).
-  N. K. Vitanov, E. Yankulova, Multifractal analysis of the longrangecorrelations in the cardiac dynamics of Drosophilamelanogaster, Chaos, Solitons & Fractals 28(3): 768-775(2006).[Crossref]
-  J. M. T. Thomson, H. B. Stewart, Nonlinear dynamics and chaos:Geometrical methods for scientists, (Wiley, New York, 1986)
-  J. S. Durbin, J. Koopman, Time series analysis by state spacemethods, (Oxford University Press, Oxford, 2012).
-  A. Vespignani, Predicting the behavior of techno-social systems,Science 325(5939): 425-428 (2009).[WoS]
-  N. K. Vitanov, M. Ausloos, G. Rotundo, Discrete model of ideologicalstruggle accounting for migration, Advances in ComplexSystems 15(S1): 1250049 (2012).[WoS][Crossref]
-  M. E. J. Newman, Power laws, Pareto distributions and Zipf’slaw, Contemporary Physics 46(5): 323-351 (2005).[Crossref]
-  J.C. Córdoba, On the distribution of city sizes, Journal of UrbanEconomics 63(1): 177–197 (2008).[Crossref][WoS]
-  C. Mladenov, E. Dimitrov, Development of the urbanization processin Bulgaria during the period between the Liberation andthe end of World War Two, Geography (in Bulgarian) 1(1): 13-17(2009).
-  B. J. L. Berry, Cities as systems within systems of cities, Papersin Regional Science 13(1): 147–163 (1964).[Crossref]
-  S. El-Shakhs, Development, primacy, and systems of cities, TheJournal of Developing Areas 7(1): 11–36 (1972).
-  B. Lyman, Colonial governance in the development of urban primacy,Studies in Comparative International Development 27(2):24–38 (1992).[Crossref]
-  C. A. Smith, Types of city-size distributions: a comparative analysis,(Clarendon Press, Oxford, 1990).
-  E. Sheppard, City size distributions and spatial economicchange. WP-82-31, Working papers of the International Institutefor Applied System Analysis, Laxenburg, Austria (1982).
-  C. Chase-Dunn, The effects of international economic dependenceon development and inequality: a cross-national study,American Sociological Review 40(6):720-738 (1975).[Crossref]
-  H.W. Richardson, Theory of the distribution of city sizes: Reviewand prospects, Regional Studies 7(3): 239-251 (1973).[Crossref]
-  P. Krugman, Confronting the mystery of urban hierarchy, Journalof the Japanese and International Economies 10(4): 99-418(1996).
-  N.K. Vitanov, Z.I. Dimitrova, Bulgarian cities and the New EconomicGeography, (Vanio Nedkov, Sofia, 2014).