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Emergence of double scaling law in complex system

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  • D. D. Han
  • J. H. Qian
  • Y. G. Ma

Abstract

We introduce a stochastic model to explain a double power-law distribution which exhibits two different Paretian behaviors in the upper and the lower tail and widely exists in social and economic systems. The model incorporates fitness consideration and noise fluctuation. We find that if the number of variables (e.g. the degree of nodes in complex networks or people's incomes) grows exponentially, normal distributed fitness coupled with exponentially increasing variable is responsible for the emergence of the double power-law distribution. Fluctuations do not change the result qualitatively but contribute to the second-part scaling exponent. The evolution of Chinese airline network is taken as an example to show a nice agreement with our stochastic model.

Suggested Citation

  • D. D. Han & J. H. Qian & Y. G. Ma, 2011. "Emergence of double scaling law in complex system," Papers 1103.2001, arXiv.org.
  • Handle: RePEc:arx:papers:1103.2001
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    3. Y. Malevergne & D. Sornette, 2002. "Investigating Extreme Dependences: Concepts and Tools," Papers cond-mat/0203166, arXiv.org.
    4. Bartram, Sohnke M. & Wang, Yaw-Huei, 2005. "Another look at the relationship between cross-market correlation and volatility," Finance Research Letters, Elsevier, vol. 2(2), pages 75-88, June.
    5. Corsetti, Giancarlo & Pericoli, Marcello & Sbracia, Massimo, 2005. "'Some contagion, some interdependence': More pitfalls in tests of financial contagion," Journal of International Money and Finance, Elsevier, vol. 24(8), pages 1177-1199, December.
    6. King, Mervyn & Sentana, Enrique & Wadhwani, Sushil, 1994. "Volatility and Links between National Stock Markets," Econometrica, Econometric Society, vol. 62(4), pages 901-933, July.
    7. Pierre Cizeau & Marc Potters & Jean-Philippe Bouchaud, 2000. "Correlation structure of extreme stock returns," Science & Finance (CFM) working paper archive 0006034, Science & Finance, Capital Fund Management.
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    Cited by:

    1. Yuan, Wei-Guo & Liu, Yun, 2015. "A mixing evolution model for bidirectional microblog user networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 432(C), pages 167-179.

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