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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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    1. Aniket Magarkar & Nawel Mele & Noha Abdel-Rahman & Sarah Butcher & Mika Torkkeli & Ritva Serimaa & Arja Paananen & Markus Linder & Alex Bunker, 2014. "Hydrophobin Film Structure for HFBI and HFBII and Mechanism for Accelerated Film Formation," PLOS Computational Biology, Public Library of Science, vol. 10(7), pages 1-13, July.
    2. 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.
    3. Feng, Shiyuan & Weng, Tongfeng & Chen, Xiaolu & Ren, Zhuoming & Su, Chang & Li, Chunzi, 2024. "Scaling law of diffusion processes on fractal networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 640(C).
    4. Raúl F. Pérez & Patricia Tezanos & Alfonso Peñarroya & Alejandro González-Ramón & Rocío G. Urdinguio & Javier Gancedo-Verdejo & Juan Ramón Tejedor & Pablo Santamarina-Ojeda & Juan José Alba-Linares & , 2024. "A multiomic atlas of the aging hippocampus reveals molecular changes in response to environmental enrichment," Nature Communications, Nature, vol. 15(1), pages 1-26, December.

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